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Theorem mo4f 2003
 Description: "At most one" expressed using implicit substitution. (Contributed by NM, 10-Apr-2004.)
Hypotheses
Ref Expression
mo4f.1
mo4f.2
Assertion
Ref Expression
mo4f
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem mo4f
StepHypRef Expression
1 ax-17 1460 . . 3
21mo3h 1996 . 2
3 mo4f.1 . . . . . 6
4 mo4f.2 . . . . . 6
53, 4sbie 1716 . . . . 5
65anbi2i 445 . . . 4
76imbi1i 236 . . 3
872albii 1401 . 2
92, 8bitri 182 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283  wnf 1390  wsb 1687  wmo 1944 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947 This theorem is referenced by:  mo4  2004  mob2  2782  moop2  4035  dffun4f  4969
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