Theorem ss2rabi

Description: Inference of restricted abstraction subclass from implication. (Contributed by NM, 14-Oct-1999) Avoid axioms. (Revised by SN, 4-Feb-2025)

	Ref	Expression
Hypothesis	ss2rabi.1	|- ( x e. A -> ( ph -> ps ) )
Assertion	ss2rabi	|- { x e. A | ph } C_ { x e. A | ps }

Proof

Step	Hyp	Ref	Expression
1		ss2rabi.1	|- ( x e. A -> ( ph -> ps ) )
2	1	adantl	|- ( ( T. /\ x e. A ) -> ( ph -> ps ) )
3	2	ss2rabdv	|- ( T. -> { x e. A | ph } C_ { x e. A | ps } )
4	3	mptru	|- { x e. A | ph } C_ { x e. A | ps }