Metamath Proof Explorer


Theorem ceqsalALT

Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. Shorter proof uses df-clab . (Contributed by NM, 18-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ceqsal.1 x ψ
ceqsal.2 A V
ceqsal.3 x = A φ ψ
Assertion ceqsalALT x x = A φ ψ

Proof

Step Hyp Ref Expression
1 ceqsal.1 x ψ
2 ceqsal.2 A V
3 ceqsal.3 x = A φ ψ
4 1 3 ceqsalg A V x x = A φ ψ
5 2 4 ax-mp x x = A φ ψ