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Theorem mo2icl 3015
 Description: Theorem for inferring "at most one." (Contributed by NM, 17-Oct-1996.)
Assertion
Ref Expression
mo2icl
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem mo2icl
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq2 2362 . . . . . 6
21imbi2d 307 . . . . 5
32albidv 1625 . . . 4
43imbi1d 308 . . 3
5 19.8a 1756 . . . 4
6 nfv 1619 . . . . 5
76mo2 2233 . . . 4
85, 7sylibr 203 . . 3
94, 8vtoclg 2914 . 2
10 vex 2862 . . . . . . 7
11 eleq1 2413 . . . . . . 7
1210, 11mpbii 202 . . . . . 6
1312imim2i 13 . . . . 5
1413con3rr3 128 . . . 4
1514alimdv 1621 . . 3
16 alnex 1543 . . . 4
17 exmo 2249 . . . . 5
1817ori 364 . . . 4
1916, 18sylbi 187 . . 3
2015, 19syl6 29 . 2
219, 20pm2.61i 156 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4  wal 1540  wex 1541   wceq 1642   wcel 1710  wmo 2205  cvv 2859 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-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: (None)
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