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Theorem mo2icl 3115
 Description: Theorem for inferring "at most one." (Contributed by NM, 17-Oct-1996.)
Assertion
Ref Expression
mo2icl
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem mo2icl
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq2 2447 . . . . . 6
21imbi2d 309 . . . . 5
32albidv 1636 . . . 4
43imbi1d 310 . . 3
5 19.8a 1763 . . . 4
6 nfv 1630 . . . . 5
76mo2 2312 . . . 4
85, 7sylibr 205 . . 3
94, 8vtoclg 3013 . 2
10 vex 2961 . . . . . . 7
11 eleq1 2498 . . . . . . 7
1210, 11mpbii 204 . . . . . 6
1312imim2i 14 . . . . 5
1413con3rr3 131 . . . 4
1514alimdv 1632 . . 3
16 alnex 1553 . . . 4
17 exmo 2328 . . . . 5
1817ori 366 . . . 4
1916, 18sylbi 189 . . 3
2015, 19syl6 32 . 2
219, 20pm2.61i 159 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1550  wex 1551   wceq 1653   wcel 1726  wmo 2284  cvv 2958 This theorem is referenced by:  invdisj  4204  opabiotafun  6539  fseqenlem2  7911  dfac2  8016  imasaddfnlem  13758  imasvscafn  13767  bnj149  29320 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960
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