Theorem rabeqdv

Description: Equality of restricted class abstractions. Deduction form of rabeq . (Contributed by Glauco Siliprandi, 5-Apr-2020)

	Ref	Expression
Hypothesis	rabeqdv.1	|- ( ph -> A = B )
Assertion	rabeqdv	|- ( ph -> { x e. A | ps } = { x e. B | ps } )

Proof

Step	Hyp	Ref	Expression
1		rabeqdv.1	|- ( ph -> A = B )
2		rabeq	|- ( A = B -> { x e. A | ps } = { x e. B | ps } )
3	1 2	syl	|- ( ph -> { x e. A | ps } = { x e. B | ps } )