Theorem eupicka 2080

Description: Version of eupick 2079 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 2010	. . 3 |- ( E! x ph -> A. x E! x ph )
2		hbe1 1472	. . 3 |- ( E. x ( ph /\ ps ) -> A. x E. x ( ph /\ ps ) )
3	1, 2	hban 1527	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( E! x ph /\ E. x ( ph /\ ps ) ) )
4		eupick 2079	. 2 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> ( ph -> ps ) )
5	3, 4	alrimih 1446	1 |- ( ( E! x ph /\ E. x ( ph /\ ps ) ) -> A. x ( ph -> ps ) )

Syntax hints:   -> wi 4   /\ wa 103   A.wal 1330   E.wex 1469   E!weu 2000

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004

This theorem is referenced by:  eupickbi  2082