Theorem eupicka 2099

Description: Version of eupick 2098 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 2029	. . 3 |- ( E! x ph -> A. x E! x ph )
2		hbe1 1488	. . 3 |- ( E. x ( ph /\ ps ) -> A. x E. x ( ph /\ ps ) )
3	1, 2	hban 1540	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( E! x ph /\ E. x ( ph /\ ps ) ) )
4		eupick 2098	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> ( ph -> ps ) )
5	3, 4	alrimih 1462	1 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( ph -> ps ) )

Syntax hints:   -> wi 4   /\ wa 103   A.wal 1346   E.wex 1485   E!weu 2019

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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-eu 2022  df-mo 2023

This theorem is referenced by:  eupickbi  2101