Theorem iedgvalprc 29557

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 3062	. 2 ⊢ (𝐶 ∉ V ↔ ¬ 𝐶 ∈ V)
2		fvprc 6865	. 2 ⊢ (¬ 𝐶 ∈ V → (iEdg‘𝐶) = ∅)
3	1, 2	sylbi 220	1 ⊢ (𝐶 ∉ V → (iEdg‘𝐶) = ∅)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   = wceq 1570   ∈ wcel 2145   ∉ wnel 3061  Vcvv 3450  ∅c0 4278  ‘cfv 6527  iEdgciedg 29508

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732  ax-nul 5259  ax-pr 5390

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-mo 2564  df-eu 2594  df-clab 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-nel 3062  df-rab 3413  df-v 3452  df-dif 3901  df-un 3903  df-ss 3915  df-nul 4279  df-if 4482  df-sn 4584  df-pr 4586  df-op 4590  df-uni 4867  df-br 5103  df-iota 6483  df-fv 6535

This theorem is used by: (None)