Theorem vtocle 3134

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.)

Hypotheses

Ref	Expression
vtocle.1	|- A e. _V
vtocle.2	|- ( x = A -> ph )

Assertion

Ref	Expression
vtocle	|- ph

Distinct variable groups:   x, A   ph, x

Proof of Theorem vtocle

Step	Hyp	Ref	Expression
1		vtocle.1	. 2 |- A e. _V
2		vtocle.2	. . 3 |- ( x = A -> ph )
3	2	vtocleg 3131	. 2 |- ( A e. _V -> ph )
4	1, 3	ax-mp 5	1 |- ph

Syntax hints:   -> wi 4   = wceq 1454   e. wcel 1897   _Vcvv 3056

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-12 1943  ax-ext 2441

This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1457  df-ex 1674  df-sb 1808  df-clab 2448  df-cleq 2454  df-clel 2457  df-v 3058

This theorem is referenced by:  zfrepclf  4534  tz6.12i  5907  eloprabga  6409  cfflb  8714  axcc3  8893  nn0ind-raph  11063  finxpreclem6  31832