Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  wcbtr GIF version

Theorem wcbtr 411
 Description: Transitive inference.
Hypotheses
Ref Expression
wcbtr.1 C (a, b) = 1
wcbtr.2 (bc) = 1
Assertion
Ref Expression
wcbtr C (a, c) = 1

Proof of Theorem wcbtr
StepHypRef Expression
1 wcbtr.1 . . . 4 C (a, b) = 1
21wdf-c2 384 . . 3 (a ≡ ((ab) ∪ (ab ))) = 1
3 wcbtr.2 . . . . 5 (bc) = 1
43wlan 370 . . . 4 ((ab) ≡ (ac)) = 1
53wr4 199 . . . . 5 (bc ) = 1
65wlan 370 . . . 4 ((ab ) ≡ (ac )) = 1
74, 6w2or 372 . . 3 (((ab) ∪ (ab )) ≡ ((ac) ∪ (ac ))) = 1
82, 7wr2 371 . 2 (a ≡ ((ac) ∪ (ac ))) = 1
98wdf-c1 383 1 C (a, c) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 8   C wcmtr 29 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  df-cmtr 134 This theorem is referenced by:  wcom2an  428  wnbdi  429  ska2  432  ska4  433  woml6  436
 Copyright terms: Public domain W3C validator