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Metamath Proof Explorer

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	$⊢ B \in V$
	Assertion	funimaex	$⊢ Fun A \to A [B] \in V$

Proof

Step	Hyp	Ref	Expression
1		zfrep5.1	$⊢ B \in V$
2		funimaexg	$⊢ (Fun A \land B \in V) \to A [B] \in V$
3	1 2	mpan2	$⊢ Fun A \to A [B] \in V$