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Theorem edgopval 26850
 Description: The edges of a graph represented as ordered pair. (Contributed by AV, 1-Jan-2020.) (Revised by AV, 13-Oct-2020.)
Assertion
Ref Expression
edgopval ((𝑉𝑊𝐸𝑋) → (Edg‘⟨𝑉, 𝐸⟩) = ran 𝐸)

Proof of Theorem edgopval
StepHypRef Expression
1 edgval 26848 . 2 (Edg‘⟨𝑉, 𝐸⟩) = ran (iEdg‘⟨𝑉, 𝐸⟩)
2 opiedgfv 26806 . . 3 ((𝑉𝑊𝐸𝑋) → (iEdg‘⟨𝑉, 𝐸⟩) = 𝐸)
32rneqd 5795 . 2 ((𝑉𝑊𝐸𝑋) → ran (iEdg‘⟨𝑉, 𝐸⟩) = ran 𝐸)
41, 3syl5eq 2871 1 ((𝑉𝑊𝐸𝑋) → (Edg‘⟨𝑉, 𝐸⟩) = ran 𝐸)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399   = wceq 1538   ∈ wcel 2115  ⟨cop 4556  ran crn 5543  ‘cfv 6343  iEdgciedg 26796  Edgcedg 26846 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pow 5253  ax-pr 5317  ax-un 7455 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-rab 3142  df-v 3482  df-sbc 3759  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-op 4557  df-uni 4825  df-br 5053  df-opab 5115  df-mpt 5133  df-id 5447  df-xp 5548  df-rel 5549  df-cnv 5550  df-co 5551  df-dm 5552  df-rn 5553  df-iota 6302  df-fun 6345  df-fv 6351  df-2nd 7685  df-iedg 26798  df-edg 26847 This theorem is referenced by:  edgov  26851  cusgrsize  27250  uspgrloopedg  27314  uspgrsprfo  44306
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