Theorem opabbi

Description: Equality deduction for class abstraction of ordered pairs. (Contributed by Giovanni Mascellani, 10-Apr-2018)

	Ref	Expression
Assertion	opabbi	|- ( A. x A. y ( ph <-> ps ) -> { <. x , y >. | ph } = { <. x , y >. | ps } )

Proof

Step	Hyp	Ref	Expression
1		eqopab2b	|- ( { <. x , y >. | ph } = { <. x , y >. | ps } <-> A. x A. y ( ph <-> ps ) )
2	1	biimpri	|- ( A. x A. y ( ph <-> ps ) -> { <. x , y >. | ph } = { <. x , y >. | ps } )