Metamath Proof Explorer


Theorem vtocle

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993) Avoid df-clab . (Revised by Wolf Lammen, 31-May-2025)

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 1 isseti
 |-  E. x x = A
4 2 3 exlimiiv
 |-  ph