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Theorem u3lemnona 667
 Description: Lemma for Kalmbach implication study.
Assertion
Ref Expression
u3lemnona ((a3 b)a ) = (a ∪ (ab ))

Proof of Theorem u3lemnona
StepHypRef Expression
1 u3lemaa 602 . . . 4 ((a3 b) ∩ a) = (a ∩ (ab))
2 oran2 92 . . . . 5 (ab) = (ab )
32lan 77 . . . 4 (a ∩ (ab)) = (a ∩ (ab ) )
41, 3ax-r2 36 . . 3 ((a3 b) ∩ a) = (a ∩ (ab ) )
5 df-a 40 . . 3 ((a3 b) ∩ a) = ((a3 b)a )
6 anor1 88 . . 3 (a ∩ (ab ) ) = (a ∪ (ab ))
74, 5, 63tr2 64 . 2 ((a3 b)a ) = (a ∪ (ab ))
87con1 66 1 ((a3 b)a ) = (a ∪ (ab ))
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →3 wi3 14 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  ax-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  u3lem13b  790
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