Theorem vtocle 3282

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 3279	. 2 |- ( A e. _V -> ph )
4	1, 3	ax-mp 5	1 |- ph

Syntax hints:   -> wi 4   = wceq 1483   e. wcel 1990   _Vcvv 3200

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-12 2047  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-v 3202

This theorem is referenced by:  zfrepclf  4777  tz6.12i  6214  eloprabga  6747  cfflb  9081  axcc3  9260  nn0ind-raph  11477  finxpreclem6  33233