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Theorem u2lem5 762
Description: Lemma for unified implication study.
Assertion
Ref Expression
u2lem5 (a ->2 (a ->2 b)) = (a ->2 b)
Proof of Theorem u2lem5
StepHypRef Expression
1 df-i2 45 . 2 (a ->2 (a ->2 b)) = ((a ->2 b) v (a' ^ (a ->2 b)'))
2 ancom 74 . . . . 5 (a' ^ (a ->2 b)') = ((a ->2 b)' ^ a')
3 u2lemnana 646 . . . . 5 ((a ->2 b)' ^ a') = 0
42, 3ax-r2 36 . . . 4 (a' ^ (a ->2 b)') = 0
54lor 70 . . 3 ((a ->2 b) v (a' ^ (a ->2 b)')) = ((a ->2 b) v 0)
6 or0 102 . . 3 ((a ->2 b) v 0) = (a ->2 b)
75, 6ax-r2 36 . 2 ((a ->2 b) v (a' ^ (a ->2 b)')) = (a ->2 b)
81, 7ax-r2 36 1 (a ->2 (a ->2 b)) = (a ->2 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  0wf 9   ->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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