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Theorem 2moex 2275
Description: Double quantification with "at most one." (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2moex (∃*xyφy∃*xφ)

Proof of Theorem 2moex
StepHypRef Expression
1 nfe1 1732 . . 3 yyφ
21nfmo 2221 . 2 y∃*xyφ
3 19.8a 1756 . . 3 (φyφ)
43moimi 2251 . 2 (∃*xyφ∃*xφ)
52, 4alrimi 1765 1 (∃*xyφy∃*xφ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540  wex 1541  ∃*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:  2eu2  2285  2eu5  2288
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