Theorem eupicka 2134

Description: Version of eupick 2133 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 2064	. . 3 |- ( E! x ph -> A. x E! x ph )
2		hbe1 1518	. . 3 |- ( E. x ( ph /\ ps ) -> A. x E. x ( ph /\ ps ) )
3	1, 2	hban 1570	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( E! x ph /\ E. x ( ph /\ ps ) ) )
4		eupick 2133	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> ( ph -> ps ) )
5	3, 4	alrimih 1492	1 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( ph -> ps ) )

Syntax hints:   -> wi 4   /\ wa 104   A.wal 1371   E.wex 1515   E!weu 2054

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-eu 2057  df-mo 2058

This theorem is referenced by:  eupickbi  2136