Theorem rnmptss

Description: The range of an operation given by the maps-to notation as a subset. (Contributed by Thierry Arnoux, 24-Sep-2017)

	Ref	Expression
Hypothesis	rnmptss.1	|- F = ( x e. A |-> B )
Assertion	rnmptss	|- ( A. x e. A B e. C -> ran F C_ C )

Proof

Step	Hyp	Ref	Expression
1		rnmptss.1	|- F = ( x e. A |-> B )
2	1	fmpt	|- ( A. x e. A B e. C <-> F : A --> C )
3		frn	|- ( F : A --> C -> ran F C_ C )
4	2 3	sylbi	|- ( A. x e. A B e. C -> ran F C_ C )