Theorem eupicka 1437

Description: Version of eupick 1436 with closed formulas.

Assertion

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

Proof of Theorem eupicka

Step	Hyp	Ref	Expression
1		hbeu1 1390	. . 3 |- (E!xph -> A.xE!xph)
2		hbe1 1018	. . 3 |- (E.x(ph /\ ps) -> A.xE.x(ph /\ ps))
3	1, 2	hban 1011	. 2 |- ((E!xph /\ E.x(ph /\ ps)) -> A.x(E!xph /\ E.x(ph /\ ps)))
4		eupick 1436	. 2 |- ((E!xph /\ E.x(ph /\ ps)) -> (ph -> ps))
5	3, 4	19.21ai 1000	1 |- ((E!xph /\ E.x(ph /\ ps)) -> A.x(ph -> ps))

Syntax hints:   -> wi 3   /\ wa 223  A.wal 956  E.wex 982  E!weu 1382

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385

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