Theorem eupicka 2268

Description: Version of eupick 2267 with closed formulas. (Contributed by NM, 6-Sep-2008.)

Assertion

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

Proof of Theorem eupicka

Step	Hyp	Ref	Expression
1		nfeu1 2214	. . 3 |- F/xE!xph
2		nfe1 1732	. . 3 |- F/xE.x(ph /\ ps)
3	1, 2	nfan 1824	. 2 |- F/x(E!xph /\ E.x(ph /\ ps))
4		eupick 2267	. 2 |- ((E!xph /\ E.x(ph /\ ps)) -> (ph -> ps))
5	3, 4	alrimi 1765	1 |- ((E!xph /\ E.x(ph /\ ps)) -> A.x(ph -> ps))

Syntax hints:   -> wi 4   /\ wa 358  A.wal 1540  E.wex 1541  E!weu 2204

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209

This theorem is referenced by:  eupickbi  2270