Metamath Proof Explorer


Theorem bj-elissetALT

Description: Alternate proof of elisset . This is essentially the same proof as seen by inlining bj-denotes and bj-denoteslem . Use elissetv instead when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 29-Apr-2019) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion bj-elissetALT
|- ( A e. V -> E. x x = A )

Proof

Step Hyp Ref Expression
1 elissetv
 |-  ( A e. V -> E. y y = A )
2 bj-denotes
 |-  ( E. y y = A <-> E. x x = A )
3 1 2 sylib
 |-  ( A e. V -> E. x x = A )