Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  u1lemoa GIF version

Theorem u1lemoa 620
 Description: Lemma for Sasaki implication study. (Contributed by NM, 14-Dec-1997.)
Assertion
Ref Expression
u1lemoa ((a1 b) ∪ a) = 1

Proof of Theorem u1lemoa
StepHypRef Expression
1 df-i1 44 . . 3 (a1 b) = (a ∪ (ab))
21ax-r5 38 . 2 ((a1 b) ∪ a) = ((a ∪ (ab)) ∪ a)
3 ax-a2 31 . . 3 ((a ∪ (ab)) ∪ a) = (a ∪ (a ∪ (ab)))
4 ax-a3 32 . . . . 5 ((aa ) ∪ (ab)) = (a ∪ (a ∪ (ab)))
54ax-r1 35 . . . 4 (a ∪ (a ∪ (ab))) = ((aa ) ∪ (ab))
6 ax-a2 31 . . . . 5 ((aa ) ∪ (ab)) = ((ab) ∪ (aa ))
7 df-t 41 . . . . . . . 8 1 = (aa )
87lor 70 . . . . . . 7 ((ab) ∪ 1) = ((ab) ∪ (aa ))
98ax-r1 35 . . . . . 6 ((ab) ∪ (aa )) = ((ab) ∪ 1)
10 or1 104 . . . . . 6 ((ab) ∪ 1) = 1
119, 10ax-r2 36 . . . . 5 ((ab) ∪ (aa )) = 1
126, 11ax-r2 36 . . . 4 ((aa ) ∪ (ab)) = 1
135, 12ax-r2 36 . . 3 (a ∪ (a ∪ (ab))) = 1
143, 13ax-r2 36 . 2 ((a ∪ (ab)) ∪ a) = 1
152, 14ax-r2 36 1 ((a1 b) ∪ a) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   →1 wi1 12 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-i1 44 This theorem is referenced by:  u1lemnana  645  oi3oa3lem1  732  i1orni1  847  oau  929
 Copyright terms: Public domain W3C validator