Metamath Proof Explorer


Theorem elexOLD

Description: Obsolete version of elex as of 28-May-2025. (Contributed by NM, 26-May-1993) (Proof shortened by Andrew Salmon, 8-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion elexOLD
|- ( A e. B -> A e. _V )

Proof

Step Hyp Ref Expression
1 exsimpl
 |-  ( E. x ( x = A /\ x e. B ) -> E. x x = A )
2 dfclel
 |-  ( A e. B <-> E. x ( x = A /\ x e. B ) )
3 isset
 |-  ( A e. _V <-> E. x x = A )
4 1 2 3 3imtr4i
 |-  ( A e. B -> A e. _V )