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Theorem u3lem5 763
Description: Lemma for unified implication study.
Assertion
Ref Expression
u3lem5 (a ->3 (a ->3 b)) = (a' v b)
Proof of Theorem u3lem5
StepHypRef Expression
1 comi31 508 . . 3 a C (a ->3 b)
21u3lemc4 703 . 2 (a ->3 (a ->3 b)) = (a' v (a ->3 b))
3 ax-a2 31 . . 3 (a' v (a ->3 b)) = ((a ->3 b) v a')
4 u3lemona 627 . . 3 ((a ->3 b) v a') = (a' v b)
53, 4ax-r2 36 . 2 (a' v (a ->3 b)) = (a' v b)
62, 5ax-r2 36 1 (a ->3 (a ->3 b)) = (a' v b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ->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:  u3lem6  767  u3lem14mp  794
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