Theorem ssopab2i

Description: Inference of ordered pair abstraction subclass from implication. (Contributed by NM, 5-Apr-1995)

	Ref	Expression
Hypothesis	ssopab2i.1	|- ( ph -> ps )
Assertion	ssopab2i	|- { <. x , y >. | ph } C_ { <. x , y >. | ps }

Proof

Step	Hyp	Ref	Expression
1		ssopab2i.1	|- ( ph -> ps )
2		ssopab2	|- ( A. x A. y ( ph -> ps ) -> { <. x , y >. | ph } C_ { <. x , y >. | ps } )
3	1	ax-gen	|- A. y ( ph -> ps )
4	2 3	mpg	|- { <. x , y >. | ph } C_ { <. x , y >. | ps }