MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  mo2icl Unicode version

Theorem mo2icl 3278
Description: Theorem for inferring "at most one." (Contributed by NM, 17-Oct-1996.)
Assertion
Ref Expression
mo2icl
Distinct variable group:   ,

Proof of Theorem mo2icl
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq2 2472 . . . . . 6
21imbi2d 316 . . . . 5
32albidv 1713 . . . 4
43imbi1d 317 . . 3
5 19.8a 1857 . . . 4
6 mo2v 2289 . . . 4
75, 6sylibr 212 . . 3
84, 7vtoclg 3167 . 2
9 eqvisset 3117 . . . . . 6
109imim2i 14 . . . . 5
1110con3rr3 136 . . . 4
1211alimdv 1709 . . 3
13 alnex 1614 . . . 4
14 exmo 2309 . . . . 5
1514ori 375 . . . 4
1613, 15sylbi 195 . . 3
1712, 16syl6 33 . 2
188, 17pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  E*wmo 2283   cvv 3109
This theorem is referenced by:  invdisj  4441  opabiotafun  5934  fseqenlem2  8427  dfac2  8532  imasaddfnlem  14925  imasvscafn  14934  bnj149  33933
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-12 1854  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  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-v 3111
  Copyright terms: Public domain W3C validator