Metamath Proof Explorer


Theorem vtocle

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

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

Proof

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