Theorem elima

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

	Ref	Expression
Hypothesis	elima.1	$$⊢A\in \mathrm{V}$$
Assertion	elima	$$⊢A\in B\left[C\right]\leftrightarrow \exists x\in CxBA$$

Proof

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