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Theorem iedgvalprc 26842
Description: Degenerated case 4 for edges: The set of indexed edges of a proper class is the empty set. (Contributed by AV, 12-Oct-2020.)
Assertion
Ref Expression
iedgvalprc (𝐶 ∉ V → (iEdg‘𝐶) = ∅)

Proof of Theorem iedgvalprc
StepHypRef Expression
1 df-nel 3119 . 2 (𝐶 ∉ V ↔ ¬ 𝐶 ∈ V)
2 fvprc 6654 . 2 𝐶 ∈ V → (iEdg‘𝐶) = ∅)
31, 2sylbi 220 1 (𝐶 ∉ V → (iEdg‘𝐶) = ∅)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1538  wcel 2115  wnel 3118  Vcvv 3480  c0 4276  cfv 6343  iEdgciedg 26793
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-nul 5196  ax-pow 5253
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-nel 3119  df-ral 3138  df-rex 3139  df-v 3482  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-iota 6302  df-fv 6351
This theorem is referenced by: (None)
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