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 ) )