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Theorem u1lem2 744
Description: Lemma for unified implication study.
Assertion
Ref Expression
u1lem2 (((a ->1 b) ->1 a) ->1 a) = 1
Proof of Theorem u1lem2
StepHypRef Expression
1 df-i1 44 . 2 (((a ->1 b) ->1 a) ->1 a) = (((a ->1 b) ->1 a)' v (((a ->1 b) ->1 a) ^ a))
2 u1lem1n 739 . . . 4 ((a ->1 b) ->1 a)' = a'
3 u1lem1 734 . . . . . 6 ((a ->1 b) ->1 a) = a
43ran 78 . . . . 5 (((a ->1 b) ->1 a) ^ a) = (a ^ a)
5 anidm 111 . . . . 5 (a ^ a) = a
64, 5ax-r2 36 . . . 4 (((a ->1 b) ->1 a) ^ a) = a
72, 62or 72 . . 3 (((a ->1 b) ->1 a)' v (((a ->1 b) ->1 a) ^ a)) = (a' v a)
8 ax-a2 31 . . . 4 (a' v a) = (a v a')
9 df-t 41 . . . . 5 1 = (a v a')
109ax-r1 35 . . . 4 (a v a') = 1
118, 10ax-r2 36 . . 3 (a' v a) = 1
127, 11ax-r2 36 . 2 (((a ->1 b) ->1 a)' v (((a ->1 b) ->1 a) ^ a)) = 1
131, 12ax-r2 36 1 (((a ->1 b) ->1 a) ->1 a) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->1 wi1 12
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-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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