Theorem iedgvalprc 28872

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 3044	. 2 ⊢ (𝐶 ∉ V ↔ ¬ 𝐶 ∈ V)
2		fvprc 6889	. 2 ⊢ (¬ 𝐶 ∈ V → (iEdg‘𝐶) = ∅)
3	1, 2	sylbi 216	1 ⊢ (𝐶 ∉ V → (iEdg‘𝐶) = ∅)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1534   ∈ wcel 2099   ∉ wnel 3043  Vcvv 3471  ∅c0 4323  ‘cfv 6548  iEdgciedg 28823

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-ext 2699  ax-nul 5306  ax-pr 5429

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2530  df-eu 2559  df-clab 2706  df-cleq 2720  df-clel 2806  df-nel 3044  df-ral 3059  df-rex 3068  df-rab 3430  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-uni 4909  df-br 5149  df-iota 6500  df-fv 6556

This theorem is referenced by: (None)

Otomatik - 173.255.232.114 CloudFlare DNS Türk Telekom DNS Google DNS Open DNS

OSZAR »