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Theorem mob2 2859
 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 983 . . 3
2 moi2.1 . . 3
31, 2syl5ibcom 154 . 2
4 nfs1v 1910 . . . . . . . 8
5 sbequ12 1744 . . . . . . . 8
64, 5mo4f 2057 . . . . . . 7
7 sp 1488 . . . . . . 7
86, 7sylbi 120 . . . . . 6
9 nfv 1508 . . . . . . . . . 10
109, 2sbhypf 2730 . . . . . . . . 9
1110anbi2d 459 . . . . . . . 8
12 eqeq2 2147 . . . . . . . 8
1311, 12imbi12d 233 . . . . . . 7
1413spcgv 2768 . . . . . 6
158, 14syl5 32 . . . . 5
1615imp 123 . . . 4
1716expd 256 . . 3
18173impia 1178 . 2
193, 18impbid 128 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   w3a 962  wal 1329   wceq 1331   wcel 1480  wsb 1735  wmo 1998 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  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683 This theorem is referenced by:  moi2  2860  mob  2861
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