Theorem eupicka 2125

Description: Version of eupick 2124 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 2055	. . 3 |- ( E! x ph -> A. x E! x ph )
2		hbe1 1509	. . 3 |- ( E. x ( ph /\ ps ) -> A. x E. x ( ph /\ ps ) )
3	1, 2	hban 1561	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( E! x ph /\ E. x ( ph /\ ps ) ) )
4		eupick 2124	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> ( ph -> ps ) )
5	3, 4	alrimih 1483	1 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( ph -> ps ) )

Syntax hints:   -> wi 4   /\ wa 104   A.wal 1362   E.wex 1506   E!weu 2045

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-eu 2048  df-mo 2049

This theorem is referenced by:  eupickbi  2127