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Theorem u5lemc1b 685
Description: Commutation theorem for relevance implication.
Assertion
Ref Expression
u5lemc1b b C (a ->5 b)
Proof of Theorem u5lemc1b
StepHypRef Expression
1 comanr2 465 . . . 4 b C (a ^ b)
2 comanr2 465 . . . 4 b C (a' ^ b)
31, 2com2or 483 . . 3 b C ((a ^ b) v (a' ^ b))
4 comanr2 465 . . . 4 b' C (a' ^ b')
54comcom6 459 . . 3 b C (a' ^ b')
63, 5com2or 483 . 2 b C (((a ^ b) v (a' ^ b)) v (a' ^ b'))
7 df-i5 48 . . 3 (a ->5 b) = (((a ^ b) v (a' ^ b)) v (a' ^ b'))
87ax-r1 35 . 2 (((a ^ b) v (a' ^ b)) v (a' ^ b')) = (a ->5 b)
96, 8cbtr 182 1 b C (a ->5 b)
Colors of variables: term
Syntax hints:   C wc 3  'wn 4   v wo 6   ^ wa 7   ->5 wi5 16
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-i5 48  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  u5lemc3  695  u5lembi  725  u5lem2  748  u5lem3  753
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