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Theorem i3lan 536
Description: WQL (Weak Quantum Logic) rule. (Contributed by NM, 7-Nov-1997.)
Hypothesis
Ref Expression
i3lan.1 (a3 b) = 1
Assertion
Ref Expression
i3lan ((ca) →3 (cb)) = 1

Proof of Theorem i3lan
StepHypRef Expression
1 i3lan.1 . . 3 (a3 b) = 1
21i3ran 535 . 2 ((ac) →3 (bc)) = 1
3 ancom 74 . 2 (ca) = (ac)
4 ancom 74 . 2 (cb) = (bc)
52, 3, 4i33tr1 529 1 ((ca) →3 (cb)) = 1
Colors of variables: term
Syntax hints:   = wb 1  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:  i32an  537
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