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Theorem u1lem5 761
Description: Lemma for unified implication study.
Assertion
Ref Expression
u1lem5 (a ->1 (a ->1 b)) = (a ->1 b)
Proof of Theorem u1lem5
StepHypRef Expression
1 df-i1 44 . 2 (a ->1 (a ->1 b)) = (a' v (a ^ (a ->1 b)))
2 ancom 74 . . . . 5 (a ^ (a ->1 b)) = ((a ->1 b) ^ a)
3 u1lemaa 600 . . . . 5 ((a ->1 b) ^ a) = (a ^ b)
42, 3ax-r2 36 . . . 4 (a ^ (a ->1 b)) = (a ^ b)
54lor 70 . . 3 (a' v (a ^ (a ->1 b))) = (a' v (a ^ b))
6 df-i1 44 . . . 4 (a ->1 b) = (a' v (a ^ b))
76ax-r1 35 . . 3 (a' v (a ^ b)) = (a ->1 b)
85, 7ax-r2 36 . 2 (a' v (a ^ (a ->1 b))) = (a ->1 b)
91, 8ax-r2 36 1 (a ->1 (a ->1 b)) = (a ->1 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->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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