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Theorem mob2 3016
 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 957 . . 3
2 moi2.1 . . 3
31, 2syl5ibcom 211 . 2
4 nfs1v 2106 . . . . . . . 8
5 sbequ12 1919 . . . . . . . 8
64, 5mo4f 2236 . . . . . . 7
7 sp 1747 . . . . . . 7
86, 7sylbi 187 . . . . . 6
9 nfv 1619 . . . . . . . . . 10
109, 2sbhypf 2904 . . . . . . . . 9
1110anbi2d 684 . . . . . . . 8
12 eqeq2 2362 . . . . . . . 8
1311, 12imbi12d 311 . . . . . . 7
1413spcgv 2939 . . . . . 6
158, 14syl5 28 . . . . 5
1615imp 418 . . . 4
1716exp3a 425 . . 3
18173impia 1148 . 2
193, 18impbid 183 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934  wal 1540   wceq 1642  wsb 1648   wcel 1710  wmo 2205 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by:  moi2  3017  mob  3018
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