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Theorem mo3 2235
 Description: Alternate definition of "at most one." Definition of [BellMachover] p. 460, except that definition has the side condition that y not occur in φ in place of our hypothesis. (Contributed by NM, 8-Mar-1995.)
Hypothesis
Ref Expression
mo3.1 yφ
Assertion
Ref Expression
mo3 (∃*xφxy((φ [y / x]φ) → x = y))
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)

Proof of Theorem mo3
StepHypRef Expression
1 mo3.1 . . 3 yφ
21mo2 2233 . 2 (∃*xφyx(φx = y))
31mo 2226 . 2 (yx(φx = y) ↔ xy((φ [y / x]φ) → x = y))
42, 3bitri 240 1 (∃*xφxy((φ [y / x]φ) → x = y))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358  ∀wal 1540  ∃wex 1541  Ⅎwnf 1544  [wsb 1648  ∃*wmo 2205 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  mo4f  2236  mopick  2266  rmo3  3133
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