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Theorem i1orni1 847
Description: Complemented antecedent lemma.
Assertion
Ref Expression
i1orni1 ((a ->1 b) v (a' ->1 b)) = 1
Proof of Theorem i1orni1
StepHypRef Expression
1 df-i1 44 . . . 4 (a' ->1 b) = (a'' v (a' ^ b))
2 ax-a1 30 . . . . . 6 a = a''
32ax-r5 38 . . . . 5 (a v (a' ^ b)) = (a'' v (a' ^ b))
43ax-r1 35 . . . 4 (a'' v (a' ^ b)) = (a v (a' ^ b))
51, 4ax-r2 36 . . 3 (a' ->1 b) = (a v (a' ^ b))
65lor 70 . 2 ((a ->1 b) v (a' ->1 b)) = ((a ->1 b) v (a v (a' ^ b)))
7 orordi 112 . . 3 ((a ->1 b) v (a v (a' ^ b))) = (((a ->1 b) v a) v ((a ->1 b) v (a' ^ b)))
8 u1lemoa 620 . . . . 5 ((a ->1 b) v a) = 1
98ax-r5 38 . . . 4 (((a ->1 b) v a) v ((a ->1 b) v (a' ^ b))) = (1 v ((a ->1 b) v (a' ^ b)))
10 or1r 105 . . . 4 (1 v ((a ->1 b) v (a' ^ b))) = 1
119, 10ax-r2 36 . . 3 (((a ->1 b) v a) v ((a ->1 b) v (a' ^ b))) = 1
127, 11ax-r2 36 . 2 ((a ->1 b) v (a v (a' ^ b))) = 1
136, 12ax-r2 36 1 ((a ->1 b) v (a' ->1 b)) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->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
This theorem depends on definitions:  df-t 41  df-f 42  df-i1 44
This theorem is referenced by:  negantlem2  849
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