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Theorem u2lemoa 621
 Description: Lemma for Dishkant implication study. (Contributed by NM, 14-Dec-1997.)
Assertion
Ref Expression
u2lemoa ((a2 b) ∪ a) = 1

Proof of Theorem u2lemoa
StepHypRef Expression
1 df-i2 45 . . 3 (a2 b) = (b ∪ (ab ))
21ax-r5 38 . 2 ((a2 b) ∪ a) = ((b ∪ (ab )) ∪ a)
3 ax-a2 31 . . 3 ((b ∪ (ab )) ∪ a) = (a ∪ (b ∪ (ab )))
4 ax-a3 32 . . . . 5 ((ab) ∪ (ab )) = (a ∪ (b ∪ (ab )))
54ax-r1 35 . . . 4 (a ∪ (b ∪ (ab ))) = ((ab) ∪ (ab ))
6 ax-a2 31 . . . . 5 ((ab) ∪ (ab )) = ((ab ) ∪ (ab))
7 oran 87 . . . . . . 7 (ab) = (ab )
87lor 70 . . . . . 6 ((ab ) ∪ (ab)) = ((ab ) ∪ (ab ) )
9 df-t 41 . . . . . . 7 1 = ((ab ) ∪ (ab ) )
109ax-r1 35 . . . . . 6 ((ab ) ∪ (ab ) ) = 1
118, 10ax-r2 36 . . . . 5 ((ab ) ∪ (ab)) = 1
126, 11ax-r2 36 . . . 4 ((ab) ∪ (ab )) = 1
135, 12ax-r2 36 . . 3 (a ∪ (b ∪ (ab ))) = 1
143, 13ax-r2 36 . 2 ((b ∪ (ab )) ∪ a) = 1
152, 14ax-r2 36 1 ((a2 b) ∪ a) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   →2 wi2 13 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-t 41  df-i2 45 This theorem is referenced by:  u2lemnana  646
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