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Theorem eupicka 2268
 Description: Version of eupick 2267 with closed formulas. (Contributed by NM, 6-Sep-2008.)
Assertion
Ref Expression
eupicka ((∃!xφ x(φ ψ)) → x(φψ))

Proof of Theorem eupicka
StepHypRef Expression
1 nfeu1 2214 . . 3 x∃!xφ
2 nfe1 1732 . . 3 xx(φ ψ)
31, 2nfan 1824 . 2 x(∃!xφ x(φ ψ))
4 eupick 2267 . 2 ((∃!xφ x(φ ψ)) → (φψ))
53, 4alrimi 1765 1 ((∃!xφ x(φ ψ)) → x(φψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wal 1540  ∃wex 1541  ∃!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
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