Metamath Proof Explorer


Theorem sbceq1d

Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017) (Revised by NM, 30-Jun-2018)

Ref Expression
Hypothesis sbceq1d.1
|- ( ph -> A = B )
Assertion sbceq1d
|- ( ph -> ( [. A / x ]. ps <-> [. B / x ]. ps ) )

Proof

Step Hyp Ref Expression
1 sbceq1d.1
 |-  ( ph -> A = B )
2 dfsbcq
 |-  ( A = B -> ( [. A / x ]. ps <-> [. B / x ]. ps ) )
3 1 2 syl
 |-  ( ph -> ( [. A / x ]. ps <-> [. B / x ]. ps ) )