Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  moim Unicode version

Theorem moim 2070
 Description: "At most one" is preserved through implication (notice wff reversal). (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
moim

Proof of Theorem moim
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfa1 1521 . . 3
2 ax-4 1490 . . . . . 6
3 spsbim 1823 . . . . . 6
42, 3anim12d 333 . . . . 5
54imim1d 75 . . . 4
65alimdv 1859 . . 3
71, 6alimd 1501 . 2
8 ax-17 1506 . . 3
98mo3h 2059 . 2
10 ax-17 1506 . . 3
1110mo3h 2059 . 2
127, 9, 113imtr4g 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1333  wsb 1742  wmo 2007 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010 This theorem is referenced by:  moimi  2071  euimmo  2073  moexexdc  2090  euexex  2091  rmoim  2913  rmoimi2  2915  ssrmof  3191  disjss1  3948  reusv1  4416  funmo  5182  uptx  12634
 Copyright terms: Public domain W3C validator