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Theorem u2lem5 762
 Description: Lemma for unified implication study. (Contributed by NM, 20-Dec-1997.)
Assertion
Ref Expression
u2lem5 (a2 (a2 b)) = (a2 b)

Proof of Theorem u2lem5
StepHypRef Expression
1 df-i2 45 . 2 (a2 (a2 b)) = ((a2 b) ∪ (a ∩ (a2 b) ))
2 ancom 74 . . . . 5 (a ∩ (a2 b) ) = ((a2 b)a )
3 u2lemnana 646 . . . . 5 ((a2 b)a ) = 0
42, 3ax-r2 36 . . . 4 (a ∩ (a2 b) ) = 0
54lor 70 . . 3 ((a2 b) ∪ (a ∩ (a2 b) )) = ((a2 b) ∪ 0)
6 or0 102 . . 3 ((a2 b) ∪ 0) = (a2 b)
75, 6ax-r2 36 . 2 ((a2 b) ∪ (a ∩ (a2 b) )) = (a2 b)
81, 7ax-r2 36 1 (a2 (a2 b)) = (a2 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  0wf 9   →2 wi2 13 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i2 45 This theorem is referenced by: (None)
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