Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  u4lemnob GIF version

Theorem u4lemnob 673
 Description: Lemma for non-tollens implication study.
Assertion
Ref Expression
u4lemnob ((a4 b)b) = ((ab ) ∪ b)

Proof of Theorem u4lemnob
StepHypRef Expression
1 u4lemanb 618 . . . 4 ((a4 b) ∩ b ) = ((ab) ∩ b )
2 oran2 92 . . . . 5 (ab) = (ab )
32ran 78 . . . 4 ((ab) ∩ b ) = ((ab )b )
41, 3ax-r2 36 . . 3 ((a4 b) ∩ b ) = ((ab )b )
5 anor1 88 . . 3 ((a4 b) ∩ b ) = ((a4 b)b)
6 anor3 90 . . 3 ((ab )b ) = ((ab ) ∪ b)
74, 5, 63tr2 64 . 2 ((a4 b)b) = ((ab ) ∪ b)
87con1 66 1 ((a4 b)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: (None)
 Copyright terms: Public domain W3C validator