Theorem dffunALTV5

Description: Alternate definition of the function relation predicate, cf. dfdisjALTV5 . (Contributed by Peter Mazsa, 5-Sep-2021)

	Ref	Expression
Assertion	dffunALTV5	|- ( FunALTV F <-> ( A. x e. ran F A. y e. ran F ( x = y \/ ( [ x ] `' F i^i [ y ] `' F ) = (/) ) /\ Rel F ) )

Proof

Step	Hyp	Ref	Expression
1		dffunALTV2	|- ( FunALTV F <-> ( ,~ F C_ _I /\ Rel F ) )
2		cossssid5	|- ( ,~ F C_ _I <-> A. x e. ran F A. y e. ran F ( x = y \/ ( [ x ] `' F i^i [ y ] `' F ) = (/) ) )
3	2	anbi1i	|- ( ( ,~ F C_ _I /\ Rel F ) <-> ( A. x e. ran F A. y e. ran F ( x = y \/ ( [ x ] `' F i^i [ y ] `' F ) = (/) ) /\ Rel F ) )
4	1 3	bitri	|- ( FunALTV F <-> ( A. x e. ran F A. y e. ran F ( x = y \/ ( [ x ] `' F i^i [ y ] `' F ) = (/) ) /\ Rel F ) )