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Theorem opiedgfvi 25790
 Description: The set of indexed edges of a graph represented as an ordered pair of vertices and indexed edges as function value. (Contributed by AV, 4-Mar-2021.)
Hypotheses
Ref Expression
opvtxfvi.v 𝑉 ∈ V
opvtxfvi.e 𝐸 ∈ V
Assertion
Ref Expression
opiedgfvi (iEdg‘⟨𝑉, 𝐸⟩) = 𝐸

Proof of Theorem opiedgfvi
StepHypRef Expression
1 opvtxfvi.v . 2 𝑉 ∈ V
2 opvtxfvi.e . 2 𝐸 ∈ V
3 opiedgfv 25787 . 2 ((𝑉 ∈ V ∧ 𝐸 ∈ V) → (iEdg‘⟨𝑉, 𝐸⟩) = 𝐸)
41, 2, 3mp2an 707 1 (iEdg‘⟨𝑉, 𝐸⟩) = 𝐸
 Colors of variables: wff setvar class Syntax hints:   = wceq 1480   ∈ wcel 1987  Vcvv 3186  ⟨cop 4154  ‘cfv 5847  iEdgciedg 25775 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-8 1989  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741  ax-nul 4749  ax-pow 4803  ax-pr 4867  ax-un 6902 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-mo 2474  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2912  df-rex 2913  df-rab 2916  df-v 3188  df-sbc 3418  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-if 4059  df-sn 4149  df-pr 4151  df-op 4155  df-uni 4403  df-br 4614  df-opab 4674  df-mpt 4675  df-id 4989  df-xp 5080  df-rel 5081  df-cnv 5082  df-co 5083  df-dm 5084  df-rn 5085  df-iota 5810  df-fun 5849  df-fv 5855  df-2nd 7114  df-iedg 25777 This theorem is referenced by:  iedgvalsnop  25834  eupth2lem3  26962  konigsberglem1  26980  konigsberglem2  26981  konigsberglem3  26982
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