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Theorem ud2lem0c 278
Description: Lemma for unified disjunction.
Assertion
Ref Expression
ud2lem0c (a ->2 b)' = (b' ^ (a v b))
Proof of Theorem ud2lem0c
StepHypRef Expression
1 df-i2 45 . . 3 (a ->2 b) = (b v (a' ^ b'))
2 oran 87 . . . 4 (b v (a' ^ b')) = (b' ^ (a' ^ b')')'
3 oran 87 . . . . . . 7 (a v b) = (a' ^ b')'
43ax-r1 35 . . . . . 6 (a' ^ b')' = (a v b)
54lan 77 . . . . 5 (b' ^ (a' ^ b')') = (b' ^ (a v b))
65ax-r4 37 . . . 4 (b' ^ (a' ^ b')')' = (b' ^ (a v b))'
72, 6ax-r2 36 . . 3 (b v (a' ^ b')) = (b' ^ (a v b))'
81, 7ax-r2 36 . 2 (a ->2 b) = (b' ^ (a v b))'
98con2 67 1 (a ->2 b)' = (b' ^ (a v b))
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i2 45
This theorem is referenced by:  wql2lem5  292  ud2lem1  563  ud2lem3  565  u2lem1  735  3vth9  812  2oalem1  825  oa43v  1028  oa63v  1032
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