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Theorem u2lemnanb 656
 Description: Lemma for Dishkant implication study. (Contributed by NM, 16-Dec-1997.)
Assertion
Ref Expression
u2lemnanb ((a2 b)b ) = ((ab) ∩ b )

Proof of Theorem u2lemnanb
StepHypRef Expression
1 u2lemob 631 . . . 4 ((a2 b) ∪ b) = ((ab ) ∪ b)
2 anor3 90 . . . . 5 (ab ) = (ab)
32ax-r5 38 . . . 4 ((ab ) ∪ b) = ((ab)b)
41, 3ax-r2 36 . . 3 ((a2 b) ∪ b) = ((ab)b)
5 oran 87 . . 3 ((a2 b) ∪ b) = ((a2 b)b )
6 oran2 92 . . 3 ((ab)b) = ((ab) ∩ b )
74, 5, 63tr2 64 . 2 ((a2 b)b ) = ((ab) ∩ b )
87con1 66 1 ((a2 b)b ) = ((ab) ∩ b )
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →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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