Theorem vtocle 1391

Description: Implicit substitution of a class for a set variable.

Hypotheses

Ref	Expression
vtocle.1	⊢ A ∈ V
vtocle.2	⊢ (x = A → φ)

Assertion

Ref	Expression
vtocle	⊢ φ

Distinct variable group(s):   x,A   φ,x

Proof of Theorem vtocle

Step	Hyp	Ref	Expression
1		vtocle.1	. 2 ⊢ A ∈ V
2		vtocle.2	. . 3 ⊢ (x = A → φ)
3	2	vtocleg 1390	. 2 ⊢ (A ∈ V → φ)
4	1, 3	ax-mp 6	1 ⊢ φ

Syntax hints:   → wi 2   = wceq 1091   ∈ wcel 1092  Vcvv 1348

This theorem is referenced by:  zfrepclf 1477  eloprabg 3035  nn0ind 4612

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-9 799  ax-12 802  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349

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