Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  wlem3.1 GIF version

Theorem wlem3.1 210
 Description: Weak analogue to lemma used in proof of Thm. 3.1 of Pavicic 1993. (Contributed by NM, 2-Sep-1997.)
Hypotheses
Ref Expression
wlem3.1.1 (ab) = b
wlem3.1.2 (ba) = 1
Assertion
Ref Expression
wlem3.1 (ab) = 1

Proof of Theorem wlem3.1
StepHypRef Expression
1 dfb 94 . . 3 (ab) = ((ab) ∪ (ab ))
2 wlem3.1.1 . . . . . 6 (ab) = b
32leoa 123 . . . . 5 (ab) = a
4 oran 87 . . . . . . . 8 (ab) = (ab )
54ax-r1 35 . . . . . . 7 (ab ) = (ab)
65, 2ax-r2 36 . . . . . 6 (ab ) = b
76con3 68 . . . . 5 (ab ) = b
83, 72or 72 . . . 4 ((ab) ∪ (ab )) = (ab )
9 ax-a2 31 . . . 4 (ab ) = (ba)
108, 9ax-r2 36 . . 3 ((ab) ∪ (ab )) = (ba)
111, 10ax-r2 36 . 2 (ab) = (ba)
12 wlem3.1.2 . 2 (ba) = 1
1311, 12ax-r2 36 1 (ab) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 8 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-b 39  df-a 40 This theorem is referenced by:  woml  211  lem3.1  443
 Copyright terms: Public domain W3C validator