Metamath Proof Explorer


Theorem moexexv

Description: "At most one" double quantification. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker moexexvw when possible. (Contributed by NM, 26-Jan-1997) (New usage is discouraged.)

Ref Expression
Assertion moexexv
|- ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) )

Proof

Step Hyp Ref Expression
1 nfv
 |-  F/ y ph
2 1 moexex
 |-  ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) )