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Theorem u4lem5n 766
 Description: Lemma for unified implication study.
Assertion
Ref Expression
u4lem5n (a4 (a4 b)) = ((ab) ∩ b )

Proof of Theorem u4lem5n
StepHypRef Expression
1 u4lem5 764 . . . 4 (a4 (a4 b)) = ((ab ) ∪ b)
2 anor3 90 . . . . 5 (ab ) = (ab)
32ax-r5 38 . . . 4 ((ab ) ∪ b) = ((ab)b)
41, 3ax-r2 36 . . 3 (a4 (a4 b)) = ((ab)b)
5 oran2 92 . . 3 ((ab)b) = ((ab) ∩ b )
64, 5ax-r2 36 . 2 (a4 (a4 b)) = ((ab) ∩ b )
76con2 67 1 (a4 (a4 b)) = ((ab) ∩ b )
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →4 wi4 15 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-i4 47  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  u4lem6  768
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