Metamath Proof Explorer

Theorem eupicka

Description: Version of eupick with closed formulas. (Contributed by NM, 6-Sep-2008)

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

Proof

Step Hyp Ref Expression
1 nfeu1 
 |-  F/ x E! x ph
2 nfe1 
 |-  F/ x E. x ( ph /\ ps )
3 1 2 nfan 
 |-  F/ x ( E! x ph /\ E. x ( ph /\ ps ) )
4 eupick 
 |-  ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> ( ph -> ps ) )
5 3 4 alrimi 
 |-  ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( ph -> ps ) )