Theorem wdomimag

Description: A set is weakly dominant over its image under any function. (Contributed by Stefan O'Rear, 14-Feb-2015) (Revised by Mario Carneiro, 25-Jun-2015)

	Ref	Expression
Assertion	wdomimag	|- ( ( Fun F /\ A e. V ) -> ( F " A ) ~<_* A )

Proof

Step	Hyp	Ref	Expression
1		funimaexg	|- ( ( Fun F /\ A e. V ) -> ( F " A ) e. _V )
2		wdomima2g	|- ( ( Fun F /\ A e. V /\ ( F " A ) e. _V ) -> ( F " A ) ~<_* A )
3	1 2	mpd3an3	|- ( ( Fun F /\ A e. V ) -> ( F " A ) ~<_* A )