Theorem vtocle 2847

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 2844	. 2 |- ( A e. _V -> ph )
4	1, 3	ax-mp 5	1 |- ph

Syntax hints:   -> wi 4   = wceq 1373   e. wcel 2176   _Vcvv 2772

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-v 2774

This theorem is referenced by:  repizf2  4206  nn0ind-raph  9490