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Theorem mo3h 2052
 Description: Alternate definition of "at most one." Definition of [BellMachover] p. 460, except that definition has the side condition that not occur in in place of our hypothesis. (Contributed by NM, 8-Mar-1995.) (New usage is discouraged.)
Hypothesis
Ref Expression
mo3h.1
Assertion
Ref Expression
mo3h
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem mo3h
StepHypRef Expression
1 mo3h.1 . . . . . . 7
21nfi 1438 . . . . . 6
32eu2 2043 . . . . 5
43imbi2i 225 . . . 4
5 df-mo 2003 . . . 4
6 anclb 317 . . . 4
74, 5, 63bitr4i 211 . . 3
8 19.38 1654 . . . . 5
9219.21 1562 . . . . . 6
109albii 1446 . . . . 5
118, 10sylibr 133 . . . 4
12 anabs5 562 . . . . . 6
13 pm3.31 260 . . . . . 6
1412, 13syl5bir 152 . . . . 5
15142alimi 1432 . . . 4
1611, 15syl 14 . . 3
177, 16sylbi 120 . 2
183simplbi2com 1420 . . 3
1918, 5sylibr 133 . 2
2017, 19impbii 125 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329  wex 1468  wsb 1735  weu 1999  wmo 2000 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003 This theorem is referenced by:  mo3  2053  mo2dc  2054  mo4f  2059  moim  2063  moimv  2065  moanim  2073  mopick  2077
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