Theorem vtocle 2838

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 2835	. 2 |- ( A e. _V -> ph )
4	1, 3	ax-mp 5	1 |- ph

Syntax hints:   -> wi 4   = wceq 1364   e. wcel 2167   _Vcvv 2763

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-v 2765

This theorem is referenced by:  repizf2  4195  nn0ind-raph  9443