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Theorem mob2 2715
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 905 . . 3
2 moi2.1 . . 3
31, 2syl5ibcom 144 . 2
4 nfs1v 1812 . . . . . . . 8  F/
5 sbequ12 1651 . . . . . . . 8
64, 5mo4f 1957 . . . . . . 7
7 sp 1398 . . . . . . 7
86, 7sylbi 114 . . . . . 6
9 nfv 1418 . . . . . . . . . 10  F/
109, 2sbhypf 2597 . . . . . . . . 9
1110anbi2d 437 . . . . . . . 8
12 eqeq2 2046 . . . . . . . 8
1311, 12imbi12d 223 . . . . . . 7
1413spcgv 2634 . . . . . 6
158, 14syl5 28 . . . . 5
1615imp 115 . . . 4
1716expd 245 . . 3
18173impia 1100 . 2
193, 18impbid 120 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   w3a 884  wal 1240   wceq 1242   wcel 1390  wsb 1642  wmo 1898
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553
This theorem is referenced by:  moi2  2716  mob  2717
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