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The edge DP-chromatic number of <i>G</i>, denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>χ</mi><mrow><mi>D</mi><mi>P</mi></mrow><mo>′</mo></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, is the minimum <i>k</i> such that <i>G</i> is edge DP-<i>k</i>-colorable. In 1999, Juvan, Mohar, and Thomas proved that the edge list chromatic number of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mn>4</mn></msub></semantics></math></inline-formula>-minor free graph <i>G</i> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mo>≥</mo><mn>3</mn></mrow></semantics></math></inline-formula> is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>. In this paper, we prove that if <i>G</i> is a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mn>4</mn></msub></semantics></math></inline-formula>-minor free graph, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>χ</mi><mrow><mi>D</mi><mi>P</mi></mrow><mo>′</mo></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>∈</mo><mrow><mo>{</mo><mo>Δ</mo><mo>,</mo><mo>Δ</mo><mo>+</mo><mn>1</mn><mo>}</mo></mrow></mrow></semantics></math></inline-formula>, and equality <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>χ</mi><mrow><mi>D</mi><mi>P</mi></mrow><mo>′</mo></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mo>Δ</mo><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> holds for some <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mn>4</mn></msub></semantics></math></inline-formula>-minor free graph <i>G</i> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mo>=</mo><mn>3</mn></mrow></semantics></math></inline-formula>. Moreover, if <i>G</i> is a planar graph with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mo>≥</mo><mn>9</mn></mrow></semantics></math></inline-formula> and with no intersecting triangles, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>χ</mi><mrow><mi>D</mi><mi>P</mi></mrow><mo>′</mo></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>.