Theorem funimaex

Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep . Axiom 39(vi) of Quine p. 284. Compare Exercise 9 of TakeutiZaring p. 29. (Contributed by NM, 17-Nov-2002)

	Ref	Expression
Hypothesis	zfrep5.1	$$⊢B\in \mathrm{V}$$
Assertion	funimaex	$$⊢\mathrm{Fun}A\to A\left[B\right]\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		zfrep5.1	$$⊢B\in \mathrm{V}$$
2		funimaexg	$$⊢\left(\mathrm{Fun}A\wedge B\in \mathrm{V}\right)\to A\left[B\right]\in \mathrm{V}$$
3	1 2	mpan2	$$⊢\mathrm{Fun}A\to A\left[B\right]\in \mathrm{V}$$