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Theorem u3lem11a 787
Description: Lemma for unified implication study.
Assertion
Ref Expression
u3lem11a (a ->3 ((b ->3 a) ->3 (a ->3 b))') = (a ->3 b')
Proof of Theorem u3lem11a
StepHypRef Expression
1 ud3lem1 570 . . . . 5 ((b ->3 a) ->3 (a ->3 b)) = (b v (b' ^ a'))
2 ancom 74 . . . . . . . 8 (b' ^ a') = (a' ^ b')
3 anor3 90 . . . . . . . 8 (a' ^ b') = (a v b)'
42, 3ax-r2 36 . . . . . . 7 (b' ^ a') = (a v b)'
54lor 70 . . . . . 6 (b v (b' ^ a')) = (b v (a v b)')
6 oran1 91 . . . . . 6 (b v (a v b)') = (b' ^ (a v b))'
75, 6ax-r2 36 . . . . 5 (b v (b' ^ a')) = (b' ^ (a v b))'
81, 7ax-r2 36 . . . 4 ((b ->3 a) ->3 (a ->3 b)) = (b' ^ (a v b))'
98con2 67 . . 3 ((b ->3 a) ->3 (a ->3 b))' = (b' ^ (a v b))
109ud3lem0a 260 . 2 (a ->3 ((b ->3 a) ->3 (a ->3 b))') = (a ->3 (b' ^ (a v b)))
11 u3lem11 786 . 2 (a ->3 (b' ^ (a v b))) = (a ->3 b')
1210, 11ax-r2 36 1 (a ->3 ((b ->3 a) ->3 (a ->3 b))') = (a ->3 b')
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->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: (None)
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