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Theorem u5lem2 748
Description: Lemma for unified implication study.
Assertion
Ref Expression
u5lem2 (((a ->5 b) ->5 a) ->5 a) = (a v ((a' ^ b) v (a' ^ b')))
Proof of Theorem u5lem2
StepHypRef Expression
1 u5lemc1b 685 . . . 4 a C ((a ->5 b) ->5 a)
21comcom 453 . . 3 ((a ->5 b) ->5 a) C a
32u5lemc4 705 . 2 (((a ->5 b) ->5 a) ->5 a) = (((a ->5 b) ->5 a)' v a)
4 u5lem1n 743 . . . 4 ((a ->5 b) ->5 a)' = ((a' ^ b) v (a' ^ b'))
54ax-r5 38 . . 3 (((a ->5 b) ->5 a)' v a) = (((a' ^ b) v (a' ^ b')) v a)
6 ax-a2 31 . . 3 (((a' ^ b) v (a' ^ b')) v a) = (a v ((a' ^ b) v (a' ^ b')))
75, 6ax-r2 36 . 2 (((a ->5 b) ->5 a)' v a) = (a v ((a' ^ b) v (a' ^ b')))
83, 7ax-r2 36 1 (((a ->5 b) ->5 a) ->5 a) = (a v ((a' ^ b) v (a' ^ b')))
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->5 wi5 16
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-i5 48  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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