Theorem iedgvalprc 26839

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

Step	Hyp	Ref	Expression
1		df-nel 3092	. 2 ⊢ (𝐶 ∉ V ↔ ¬ 𝐶 ∈ V)
2		fvprc 6638	. 2 ⊢ (¬ 𝐶 ∈ V → (iEdg‘𝐶) = ∅)
3	1, 2	sylbi 220	1 ⊢ (𝐶 ∉ V → (iEdg‘𝐶) = ∅)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1538   ∈ wcel 2111   ∉ wnel 3091  Vcvv 3441  ∅c0 4243  ‘cfv 6324  iEdgciedg 26790

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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-nul 5174  ax-pow 5231

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 2070  df-mo 2598  df-eu 2629  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-nel 3092  df-ral 3111  df-rex 3112  df-v 3443  df-dif 3884  df-un 3886  df-in 3888  df-ss 3898  df-nul 4244  df-if 4426  df-sn 4526  df-pr 4528  df-op 4532  df-uni 4801  df-br 5031  df-iota 6283  df-fv 6332

This theorem is referenced by: (None)