Theorem sbceq1dd

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

	Ref	Expression
Hypotheses	sbceq1d.1	|- ( ph -> A = B )
	sbceq1dd.2	|- ( ph -> [. A / x ]. ps )
Assertion	sbceq1dd	|- ( ph -> [. B / x ]. ps )

Proof

Step	Hyp	Ref	Expression
1		sbceq1d.1	|- ( ph -> A = B )
2		sbceq1dd.2	|- ( ph -> [. A / x ]. ps )
3	1	sbceq1d	|- ( ph -> ( [. A / x ]. ps <-> [. B / x ]. ps ) )
4	2 3	mpbid	|- ( ph -> [. B / x ]. ps )