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Theorem i3ran 535
Description: WQL (Weak Quantum Logic) rule.
Hypothesis
Ref Expression
i3ran.1 (a ->3 b) = 1
Assertion
Ref Expression
i3ran ((a ^ c) ->3 (b ^ c)) = 1
Proof of Theorem i3ran
StepHypRef Expression
1 i3ran.1 . . . . 5 (a ->3 b) = 1
21binr1 517 . . . 4 (b' ->3 a') = 1
32i3ror 532 . . 3 ((b' v c') ->3 (a' v c')) = 1
43binr1 517 . 2 ((a' v c')' ->3 (b' v c')') = 1
5 df-a 40 . 2 (a ^ c) = (a' v c')'
6 df-a 40 . 2 (b ^ c) = (b' v c')'
74, 5, 6i33tr1 529 1 ((a ^ c) ->3 (b ^ c)) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->3 wi3 14
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-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  i3lan  536  i32an  537
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