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Theorem wcbtr 411
Description: Transitive inference.
Hypotheses
Ref Expression
wcbtr.1 C (a, b) = 1
wcbtr.2 (b == c) = 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 == ((a ^ b) v (a ^ b'))) = 1
3 wcbtr.2 . . . . 5 (b == c) = 1
43wlan 370 . . . 4 ((a ^ b) == (a ^ c)) = 1
53wr4 199 . . . . 5 (b' == c') = 1
65wlan 370 . . . 4 ((a ^ b') == (a ^ c')) = 1
74, 6w2or 372 . . 3 (((a ^ b) v (a ^ b')) == ((a ^ c) v (a ^ c'))) = 1
82, 7wr2 371 . 2 (a == ((a ^ c) v (a ^ c'))) = 1
98wdf-c1 383 1 C (a, c) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v 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
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