Theorem vtocle 1858

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

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 1855	. 2 |- (A e. V -> ph)
4	1, 3	ax-mp 7	1 |- ph

Syntax hints:   -> wi 3   = wceq 956   e. wcel 958  Vcvv 1811

This theorem is referenced by:  zfrepclf 2699  eloprabg 4007  ac6lem 4754  nn0ind-raph 6214  elo 10444

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812

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