Theorem dffunALTV3

Description: Alternate definition of the function relation predicate, cf. dfdisjALTV3 . Reproduction of dffun2 . For the X axis and the Y axis you can convert the right side to ( A. x1 A. y1 A. y2 ( ( x1 f y1 /\ x1 f y2 ) -> y1 = y2 ) /\ Rel F ) . (Contributed by NM, 29-Dec-1996)

	Ref	Expression
Assertion	dffunALTV3	|- ( FunALTV F <-> ( A. u A. x A. y ( ( u F x /\ u F y ) -> x = y ) /\ Rel F ) )

Proof

Step	Hyp	Ref	Expression
1		dffunALTV2	|- ( FunALTV F <-> ( ,~ F C_ _I /\ Rel F ) )
2		cossssid3	|- ( ,~ F C_ _I <-> A. u A. x A. y ( ( u F x /\ u F y ) -> x = y ) )
3	2	anbi1i	|- ( ( ,~ F C_ _I /\ Rel F ) <-> ( A. u A. x A. y ( ( u F x /\ u F y ) -> x = y ) /\ Rel F ) )
4	1 3	bitri	|- ( FunALTV F <-> ( A. u A. x A. y ( ( u F x /\ u F y ) -> x = y ) /\ Rel F ) )