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Theorem mo3h 1950
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 1348 . . . . . 6  F/
32eu2 1941 . . . . 5
43imbi2i 215 . . . 4
5 df-mo 1901 . . . 4
6 anclb 302 . . . 4
74, 5, 63bitr4i 201 . . 3
8 19.38 1563 . . . . 5
9219.21 1472 . . . . . 6
109albii 1356 . . . . 5
118, 10sylibr 137 . . . 4
12 anabs5 507 . . . . . 6
13 pm3.31 249 . . . . . 6
1412, 13syl5bir 142 . . . . 5
15142alimi 1342 . . . 4
1611, 15syl 14 . . 3
177, 16sylbi 114 . 2
183simplbi2com 1330 . . 3
1918, 5sylibr 137 . 2
2017, 19impbii 117 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240  wex 1378  wsb 1642  weu 1897  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-bnd 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:  mo3  1951  mo2dc  1952  mo4f  1957  moim  1961  moimv  1963  moanim  1971  mopick  1975
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