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Theorem u2lem2 745
Description: Lemma for unified implication study.
Assertion
Ref Expression
u2lem2 (((a ->2 b) ->2 a) ->2 a) = 1
Proof of Theorem u2lem2
StepHypRef Expression
1 df-i2 45 . 2 (((a ->2 b) ->2 a) ->2 a) = (a v (((a ->2 b) ->2 a)' ^ a'))
2 u2lem1n 740 . . . . . 6 ((a ->2 b) ->2 a)' = a'
32ran 78 . . . . 5 (((a ->2 b) ->2 a)' ^ a') = (a' ^ a')
4 anidm 111 . . . . 5 (a' ^ a') = a'
53, 4ax-r2 36 . . . 4 (((a ->2 b) ->2 a)' ^ a') = a'
65lor 70 . . 3 (a v (((a ->2 b) ->2 a)' ^ a')) = (a v a')
7 df-t 41 . . . 4 1 = (a v a')
87ax-r1 35 . . 3 (a v a') = 1
96, 8ax-r2 36 . 2 (a v (((a ->2 b) ->2 a)' ^ a')) = 1
101, 9ax-r2 36 1 (((a ->2 b) ->2 a) ->2 a) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i2 45
This theorem is referenced by: (None)
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