Theorem bj-elisset

Description: Remove from elisset dependency on ax-ext (and on df-cleq and df-v ). This proof uses only df-clab and df-clel on top of first-order logic. It only requires ax-1--7 and sp . Use elissetv instead when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 29-Apr-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-elisset	$$⊢A\in V\to \exists xx=A$$

Proof

Step	Hyp	Ref	Expression
1		elissetv	$$⊢A\in V\to \exists yy=A$$
2		bj-denotes	$$⊢\exists yy=A\leftrightarrow \exists xx=A$$
3	1 2	sylib	$$⊢A\in V\to \exists xx=A$$