Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  caovord3 Unicode version

Theorem caovord3 5699
 Description: Ordering law. (Contributed by NM, 29-Feb-1996.)
Hypotheses
Ref Expression
caovord.1
caovord.2
caovord.3
caovord2.3
caovord2.com
caovord3.4
Assertion
Ref Expression
caovord3
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovord3
StepHypRef Expression
1 caovord.1 . . . . 5
2 caovord2.3 . . . . 5
3 caovord.3 . . . . 5
4 caovord.2 . . . . 5
5 caovord2.com . . . . 5
61, 2, 3, 4, 5caovord2 5698 . . . 4
76adantr 270 . . 3
8 breq1 3790 . . 3
97, 8sylan9bb 450 . 2
10 caovord3.4 . . . 4
1110, 4, 3caovord 5697 . . 3
1211ad2antlr 473 . 2
139, 12bitr4d 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285   wcel 1434  cvv 2602   class class class wbr 3787  (class class class)co 5537 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-sn 3406  df-pr 3407  df-op 3409  df-uni 3604  df-br 3788  df-iota 4891  df-fv 4934  df-ov 5540 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator