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Theorem mob2 3279
 Description: Consequence of "at most one." (Contributed by NM, 2-Jan-2015.)
Hypothesis
Ref Expression
moi2.1
Assertion
Ref Expression
mob2
Distinct variable groups:   ,   ,

Proof of Theorem mob2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 simp3 998 . . 3
2 moi2.1 . . 3
31, 2syl5ibcom 220 . 2
4 nfs1v 2181 . . . . . . . 8
5 sbequ12 1992 . . . . . . . 8
64, 5mo4f 2336 . . . . . . 7
7 sp 1859 . . . . . . 7
86, 7sylbi 195 . . . . . 6
9 nfv 1707 . . . . . . . . . 10
109, 2sbhypf 3156 . . . . . . . . 9
1110anbi2d 703 . . . . . . . 8
12 eqeq2 2472 . . . . . . . 8
1311, 12imbi12d 320 . . . . . . 7
1413spcgv 3194 . . . . . 6
158, 14syl5 32 . . . . 5
1615imp 429 . . . 4
1716expd 436 . . 3
18173impia 1193 . 2
193, 18impbid 191 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  A.wal 1393  =wceq 1395  [wsb 1739  e.wcel 1818  E*wmo 2283 This theorem is referenced by:  moi2  3280  mob  3281  rmob2  3432 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111
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