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Theorem mo3 1937
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
21nfri 1394 . 2 (φyφ)
32mo3h 1936 1 (∃*xφxy((φ [y / x]φ) → x = y))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98  wal 1226  wnf 1329  [wsb 1628  ∃*wmo 1884
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1364  ax-ie2 1365  ax-8 1377  ax-10 1378  ax-11 1379  ax-i12 1380  ax-bnd 1381  ax-4 1382  ax-17 1401  ax-i9 1405  ax-ial 1410  ax-i5r 1411
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1629  df-eu 1886  df-mo 1887
This theorem is referenced by:  sbmo  1942  rmo3  2825  isarep2  4910
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