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Theorem wcom2an 428
Description: Th. 4.2 Beran p. 49.
Hypotheses
Ref Expression
wfh.1 C (a, b) = 1
wfh.2 C (a, c) = 1
Assertion
Ref Expression
wcom2an C (a, (b ^ c)) = 1
Proof of Theorem wcom2an
StepHypRef Expression
1 wfh.1 . . . . 5 C (a, b) = 1
21wcomcom4 417 . . . 4 C (a', b') = 1
3 wfh.2 . . . . 5 C (a, c) = 1
43wcomcom4 417 . . . 4 C (a', c') = 1
52, 4wcom2or 427 . . 3 C (a', (b' v c')) = 1
6 df-a 40 . . . . . 6 (b ^ c) = (b' v c')'
76con2 67 . . . . 5 (b ^ c)' = (b' v c')
87ax-r1 35 . . . 4 (b' v c') = (b ^ c)'
98bi1 118 . . 3 ((b' v c') == (b ^ c)') = 1
105, 9wcbtr 411 . 2 C (a', (b ^ c)') = 1
1110wcomcom5 420 1 C (a, (b ^ c)) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   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:  ska4  433
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