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Theorem 2eumo 2277
Description: Double quantification with existential uniqueness and "at most one." (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eumo (∃!x∃*yφ∃*x∃!yφ)

Proof of Theorem 2eumo
StepHypRef Expression
1 euimmo 2253 . 2 (x(∃!yφ∃*yφ) → (∃!x∃*yφ∃*x∃!yφ))
2 eumo 2244 . 2 (∃!yφ∃*yφ)
31, 2mpg 1548 1 (∃!x∃*yφ∃*x∃!yφ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ∃!weu 2204  ∃*wmo 2205
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: (None)
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