Metamath Proof Explorer

Theorem 19.29

Description: Theorem 19.29 of Margaris p. 90. See also 19.29r . (Contributed by NM, 21-Jun-1993) (Proof shortened by Andrew Salmon, 13-May-2011)

Ref Expression
Assertion 19.29 
|- ( ( A. x ph /\ E. x ps ) -> E. x ( ph /\ ps ) )

Proof

Step Hyp Ref Expression
1 pm3.2 
 |-  ( ph -> ( ps -> ( ph /\ ps ) ) )
2 1 aleximi 
 |-  ( A. x ph -> ( E. x ps -> E. x ( ph /\ ps ) ) )
3 2 imp 
 |-  ( ( A. x ph /\ E. x ps ) -> E. x ( ph /\ ps ) )