Metamath Proof Explorer

Theorem spvv

Description: Specialization, using implicit substitution. Version of spv with a disjoint variable condition, which does not require ax-7 , ax-12 , ax-13 . (Contributed by NM, 30-Aug-1993) (Revised by BJ, 31-May-2019)

Ref Expression
Hypothesis spvv.1 x = y φ ψ
Assertion spvv x φ ψ


Step Hyp Ref Expression
1 spvv.1 x = y φ ψ
2 1 biimpd x = y φ ψ
3 2 spimvw x φ ψ