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Theorem i1orni1 847
 Description: Complemented antecedent lemma. (Contributed by NM, 6-Aug-2001.)
Assertion
Ref Expression
i1orni1 ((a1 b) ∪ (a1 b)) = 1

Proof of Theorem i1orni1
StepHypRef Expression
1 df-i1 44 . . . 4 (a1 b) = (a ∪ (ab))
2 ax-a1 30 . . . . . 6 a = a
32ax-r5 38 . . . . 5 (a ∪ (ab)) = (a ∪ (ab))
43ax-r1 35 . . . 4 (a ∪ (ab)) = (a ∪ (ab))
51, 4ax-r2 36 . . 3 (a1 b) = (a ∪ (ab))
65lor 70 . 2 ((a1 b) ∪ (a1 b)) = ((a1 b) ∪ (a ∪ (ab)))
7 orordi 112 . . 3 ((a1 b) ∪ (a ∪ (ab))) = (((a1 b) ∪ a) ∪ ((a1 b) ∪ (ab)))
8 u1lemoa 620 . . . . 5 ((a1 b) ∪ a) = 1
98ax-r5 38 . . . 4 (((a1 b) ∪ a) ∪ ((a1 b) ∪ (ab))) = (1 ∪ ((a1 b) ∪ (ab)))
10 or1r 105 . . . 4 (1 ∪ ((a1 b) ∪ (ab))) = 1
119, 10ax-r2 36 . . 3 (((a1 b) ∪ a) ∪ ((a1 b) ∪ (ab))) = 1
127, 11ax-r2 36 . 2 ((a1 b) ∪ (a ∪ (ab))) = 1
136, 12ax-r2 36 1 ((a1 b) ∪ (a1 b)) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ 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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