Theorem fnoprab

Description: Functionality and domain of an operation class abstraction. (Contributed by NM, 15-May-1995)

	Ref	Expression
Hypothesis	fnoprab.1	|- ( ph -> E! z ps )
Assertion	fnoprab	|- { <. <. x , y >. , z >. | ( ph /\ ps ) } Fn { <. x , y >. | ph }

Proof

Step	Hyp	Ref	Expression
1		fnoprab.1	|- ( ph -> E! z ps )
2	1	gen2	|- A. x A. y ( ph -> E! z ps )
3		fnoprabg	|- ( A. x A. y ( ph -> E! z ps ) -> { <. <. x , y >. , z >. | ( ph /\ ps ) } Fn { <. x , y >. | ph } )
4	2 3	ax-mp	|- { <. <. x , y >. , z >. | ( ph /\ ps ) } Fn { <. x , y >. | ph }