Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  u2lemonb GIF version

Theorem u2lemonb 636
 Description: Lemma for Dishkant implication study. (Contributed by NM, 15-Dec-1997.)
Assertion
Ref Expression
u2lemonb ((a2 b) ∪ b ) = 1

Proof of Theorem u2lemonb
StepHypRef Expression
1 df-i2 45 . . 3 (a2 b) = (b ∪ (ab ))
21ax-r5 38 . 2 ((a2 b) ∪ b ) = ((b ∪ (ab )) ∪ b )
3 or32 82 . . 3 ((b ∪ (ab )) ∪ b ) = ((bb ) ∪ (ab ))
4 ax-a2 31 . . . 4 ((bb ) ∪ (ab )) = ((ab ) ∪ (bb ))
5 df-t 41 . . . . . . 7 1 = (bb )
65lor 70 . . . . . 6 ((ab ) ∪ 1) = ((ab ) ∪ (bb ))
76ax-r1 35 . . . . 5 ((ab ) ∪ (bb )) = ((ab ) ∪ 1)
8 or1 104 . . . . 5 ((ab ) ∪ 1) = 1
97, 8ax-r2 36 . . . 4 ((ab ) ∪ (bb )) = 1
104, 9ax-r2 36 . . 3 ((bb ) ∪ (ab )) = 1
113, 10ax-r2 36 . 2 ((b ∪ (ab )) ∪ b ) = 1
122, 11ax-r2 36 1 ((a2 b) ∪ b ) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   →2 wi2 13 This theorem was proved from axioms:  ax-a2 31  ax-a3 32  ax-a4 33  ax-r1 35  ax-r2 36  ax-r5 38 This theorem depends on definitions:  df-t 41  df-i2 45 This theorem is referenced by:  u2lemnab  651  u2lem3  750  oa23  936
 Copyright terms: Public domain W3C validator