Theorem eupicka 2094

Description: Version of eupick 2093 with closed formulas. (Contributed by NM, 6-Sep-2008.)

Assertion

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

Proof of Theorem eupicka

Step	Hyp	Ref	Expression
1		hbeu1 2024	. . 3 |- ( E! x ph -> A. x E! x ph )
2		hbe1 1483	. . 3 |- ( E. x ( ph /\ ps ) -> A. x E. x ( ph /\ ps ) )
3	1, 2	hban 1535	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( E! x ph /\ E. x ( ph /\ ps ) ) )
4		eupick 2093	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> ( ph -> ps ) )
5	3, 4	alrimih 1457	1 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( ph -> ps ) )

Syntax hints:   -> wi 4   /\ wa 103   A.wal 1341   E.wex 1480   E!weu 2014

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-eu 2017  df-mo 2018

This theorem is referenced by:  eupickbi  2096