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Theorem i3th8 550
Description: Theorem for Kalmbach implication.
Assertion
Ref Expression
i3th8 ((a ->3 b)' ->3 ((a ->3 b) ->3 a)) = 1
Proof of Theorem i3th8
StepHypRef Expression
1 leo 158 . . 3 (a ->3 b)' =< ((a ->3 b)' v a)
2 lem4 511 . . . . 5 ((a ->3 b) ->3 ((a ->3 b) ->3 a)) = ((a ->3 b)' v a)
32ax-r1 35 . . . 4 ((a ->3 b)' v a) = ((a ->3 b) ->3 ((a ->3 b) ->3 a))
4 i3abs3 524 . . . 4 ((a ->3 b) ->3 ((a ->3 b) ->3 a)) = ((a ->3 b) ->3 a)
53, 4ax-r2 36 . . 3 ((a ->3 b)' v a) = ((a ->3 b) ->3 a)
61, 5lbtr 139 . 2 (a ->3 b)' =< ((a ->3 b) ->3 a)
76lei3 246 1 ((a ->3 b)' ->3 ((a ->3 b) ->3 a)) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6  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: (None)
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