Theorem elex2OLD

Description: Obsolete version of elex2 as of 30-Nov-2024. (Contributed by Alan Sare, 25-Sep-2011) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	elex2OLD	$$⊢A\in B\to \exists xx\in B$$

Proof

Step	Hyp	Ref	Expression
1		eleq1a	$$⊢A\in B\to \left(x=A\to x\in B\right)$$
2	1	alrimiv	$$⊢A\in B\to \forall x\left(x=A\to x\in B\right)$$
3		elisset	$$⊢A\in B\to \exists xx=A$$
4		exim	$$⊢\forall x\left(x=A\to x\in B\right)\to \left(\exists xx=A\to \exists xx\in B\right)$$
5	2 3 4	sylc	$$⊢A\in B\to \exists xx\in B$$