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Theorem mob 3018
 Description: Equality implied by "at most one." (Contributed by NM, 18-Feb-2006.)
Hypotheses
Ref Expression
moi.1
moi.2
Assertion
Ref Expression
mob
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem mob
StepHypRef Expression
1 elex 2867 . . . . 5
2 nfcv 2489 . . . . . . . 8
3 nfv 1619 . . . . . . . . . 10
4 nfmo1 2215 . . . . . . . . . 10
5 nfv 1619 . . . . . . . . . 10
63, 4, 5nf3an 1827 . . . . . . . . 9
7 nfv 1619 . . . . . . . . 9
86, 7nfim 1813 . . . . . . . 8
9 moi.1 . . . . . . . . . 10
1093anbi3d 1258 . . . . . . . . 9
11 eqeq1 2359 . . . . . . . . . 10
1211bibi1d 310 . . . . . . . . 9
1310, 12imbi12d 311 . . . . . . . 8
14 moi.2 . . . . . . . . 9
1514mob2 3016 . . . . . . . 8
162, 8, 13, 15vtoclgf 2913 . . . . . . 7
1716com12 27 . . . . . 6
18173expib 1154 . . . . 5
191, 18syl 15 . . . 4
2019com3r 73 . . 3
2120imp 418 . 2
22213impib 1149 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934   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-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:  moi  3019  rmob  3134
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