Metamath Proof Explorer


Theorem vtoclef

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 18-Aug-1993)

Ref Expression
Hypotheses vtoclef.1 x φ
vtoclef.2 A V
vtoclef.3 x = A φ
Assertion vtoclef φ

Proof

Step Hyp Ref Expression
1 vtoclef.1 x φ
2 vtoclef.2 A V
3 vtoclef.3 x = A φ
4 2 isseti x x = A
5 1 3 exlimi x x = A φ
6 4 5 ax-mp φ