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Theorem ud1lem0c 277
Description: Lemma for unified disjunction.
Assertion
Ref Expression
ud1lem0c (a ->1 b)' = (a ^ (a' v b'))
Proof of Theorem ud1lem0c
StepHypRef Expression
1 df-i1 44 . . 3 (a ->1 b) = (a' v (a ^ b))
2 df-a 40 . . . . . 6 (a ^ (a' v b')) = (a' v (a' v b')')'
3 df-a 40 . . . . . . . . 9 (a ^ b) = (a' v b')'
43ax-r1 35 . . . . . . . 8 (a' v b')' = (a ^ b)
54lor 70 . . . . . . 7 (a' v (a' v b')') = (a' v (a ^ b))
65ax-r4 37 . . . . . 6 (a' v (a' v b')')' = (a' v (a ^ b))'
72, 6ax-r2 36 . . . . 5 (a ^ (a' v b')) = (a' v (a ^ b))'
87ax-r1 35 . . . 4 (a' v (a ^ b))' = (a ^ (a' v b'))
98con3 68 . . 3 (a' v (a ^ b)) = (a ^ (a' v b'))'
101, 9ax-r2 36 . 2 (a ->1 b) = (a ^ (a' v b'))'
1110con2 67 1 (a ->1 b)' = (a ^ (a' v 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-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i1 44
This theorem is referenced by:  ud1lem1  560  ud1lem3  562  u1lemc6  706  u1lem11  780  i1abs  801  sa5  836  elimcons2  869  kb10iii  893
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