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Theorem mob2 3114
 Description: Consequence of "at most one." (Contributed by NM, 2-Jan-2015.)
Hypothesis
Ref Expression
moi2.1
Assertion
Ref Expression
mob2
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem mob2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 simp3 959 . . 3
2 moi2.1 . . 3
31, 2syl5ibcom 212 . 2
4 nfs1v 2182 . . . . . . . 8
5 sbequ12 1944 . . . . . . . 8
64, 5mo4f 2313 . . . . . . 7
7 sp 1763 . . . . . . 7
86, 7sylbi 188 . . . . . 6
9 nfv 1629 . . . . . . . . . 10
109, 2sbhypf 3001 . . . . . . . . 9
1110anbi2d 685 . . . . . . . 8
12 eqeq2 2445 . . . . . . . 8
1311, 12imbi12d 312 . . . . . . 7
1413spcgv 3036 . . . . . 6
158, 14syl5 30 . . . . 5
1615imp 419 . . . 4
1716exp3a 426 . . 3
18173impia 1150 . 2
193, 18impbid 184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wal 1549   wceq 1652  wsb 1658   wcel 1725  wmo 2282 This theorem is referenced by:  moi2  3115  mob  3116 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958
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