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Theorem opiedgfvi 26111
 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 26108 . 2 ((𝑉 ∈ V ∧ 𝐸 ∈ V) → (iEdg‘⟨𝑉, 𝐸⟩) = 𝐸)
41, 2, 3mp2an 672 1 (iEdg‘⟨𝑉, 𝐸⟩) = 𝐸
 Colors of variables: wff setvar class Syntax hints:   = wceq 1631   ∈ wcel 2145  Vcvv 3351  ⟨cop 4323  ‘cfv 6030  iEdgciedg 26096 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-8 2147  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4916  ax-nul 4924  ax-pow 4975  ax-pr 5035  ax-un 7100 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-eu 2622  df-mo 2623  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-rex 3067  df-rab 3070  df-v 3353  df-sbc 3588  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-if 4227  df-sn 4318  df-pr 4320  df-op 4324  df-uni 4576  df-br 4788  df-opab 4848  df-mpt 4865  df-id 5158  df-xp 5256  df-rel 5257  df-cnv 5258  df-co 5259  df-dm 5260  df-rn 5261  df-iota 5993  df-fun 6032  df-fv 6038  df-2nd 7320  df-iedg 26098 This theorem is referenced by:  iedgvalsnop  26155  vtxdgop  26601  vtxdginducedm1lem1  26670  finsumvtxdg2size  26681  eupth2lem3  27416  konigsberglem1  27432  konigsberglem2  27433  konigsberglem3  27434
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