Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  mo3 GIF version

Theorem mo3 1951
 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 1409 . 2 (φyφ)
32mo3h 1950 1 (∃*xφxy((φ [y / x]φ) → x = y))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98  ∀wal 1240  Ⅎwnf 1346  [wsb 1642  ∃*wmo 1898 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901 This theorem is referenced by:  sbmo  1956  rmo3  2843  isarep2  4929
 Copyright terms: Public domain W3C validator