Theorem funex

Description: If the domain of a function exists, so does the function. Part of Theorem 4.15(v) of Monk1 p. 46. This theorem is derived using the Axiom of Replacement in the form of fnex . (Note: Any resemblance between F.U.N.E.X. and "Have You Any Eggs" is purely a coincidence originated by Swedish chefs.) (Contributed by NM, 11-Nov-1995)

	Ref	Expression
Assertion	funex	|- ( ( Fun F /\ dom F e. B ) -> F e. _V )

Proof

Step	Hyp	Ref	Expression
1		funfn	|- ( Fun F <-> F Fn dom F )
2		fnex	|- ( ( F Fn dom F /\ dom F e. B ) -> F e. _V )
3	1 2	sylanb	|- ( ( Fun F /\ dom F e. B ) -> F e. _V )