QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  wle3tr1 Unicode version
Theorem wle3tr1 399
Description: Transitive inference useful for introducing definitions.
Hypotheses
Ref Expression
wle3tr1.1 (a =<2 b) = 1
wle3tr1.2 (c == a) = 1
wle3tr1.3 (d == b) = 1
Assertion
Ref Expression
wle3tr1 (c =<2 d) = 1
Proof of Theorem wle3tr1
StepHypRef Expression
1 wle3tr1.2 . . 3 (c == a) = 1
2 wle3tr1.1 . . 3 (a =<2 b) = 1
31, 2wbltr 397 . 2 (c =<2 b) = 1
4 wle3tr1.3 . . 3 (d == b) = 1
54wr1 197 . 2 (b == d) = 1
63, 5wlbtr 398 1 (c =<2 d) = 1
Colors of variables: term
Syntax hints:   = wb 1   == tb 5  1wt 8   =<2 wle2 10
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131
This theorem is referenced by:  wle3tr2  400  wle2or  403  wle2an  404
  Copyright terms: Public domain W3C validator