Theorem rabeqi

Description: Equality theorem for restricted class abstractions. Inference form of rabeqf . (Contributed by Glauco Siliprandi, 26-Jun-2021) Avoid ax-10 , ax-11 , ax-12 . (Revised by Gino Giotto, 3-Jun-2024)

	Ref	Expression
Hypothesis	rabeqi.1	|- A = B
Assertion	rabeqi	|- { x e. A | ph } = { x e. B | ph }

Proof

Step	Hyp	Ref	Expression
1		rabeqi.1	|- A = B
2	1	eleq2i	|- ( x e. A <-> x e. B )
3	2	anbi1i	|- ( ( x e. A /\ ph ) <-> ( x e. B /\ ph ) )
4	3	rabbia2	|- { x e. A | ph } = { x e. B | ph }