Theorem fvmptndm

Description: Value of a function given by the maps-to notation, outside of its domain. (Contributed by AV, 31-Dec-2020)

	Ref	Expression
Hypothesis	fvmptndm.1	|- F = ( x e. A |-> B )
Assertion	fvmptndm	|- ( -. X e. A -> ( F ` X ) = (/) )

Proof

Step	Hyp	Ref	Expression
1		fvmptndm.1	|- F = ( x e. A |-> B )
2		df-mpt	|- ( x e. A |-> B ) = { <. x , y >. | ( x e. A /\ y = B ) }
3	1 2	eqtri	|- F = { <. x , y >. | ( x e. A /\ y = B ) }
4	3	fvopab4ndm	|- ( -. X e. A -> ( F ` X ) = (/) )