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Metamath Proof Explorer

Theorem elima

Description: Membership in an image. Theorem 34 of Suppes p. 65. (Contributed by NM, 19-Apr-2004)

		Ref	Expression
	Hypothesis	elima.1	$⊢ A \in V$
	Assertion	elima	$⊢ A \in B [C] \leftrightarrow \exists x \in C x B A$

Step	Hyp	Ref	Expression
1		elima.1	$⊢ A \in V$
2		elimag	$⊢ A \in V \to (A \in B [C] \leftrightarrow \exists x \in C x B A)$
3	1 2	ax-mp	$⊢ A \in B [C] \leftrightarrow \exists x \in C x B A$