Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  u5lem2 GIF version

Theorem u5lem2 748
 Description: Lemma for unified implication study.
Assertion
Ref Expression
u5lem2 (((a5 b) →5 a) →5 a) = (a ∪ ((ab) ∪ (ab )))

Proof of Theorem u5lem2
StepHypRef Expression
1 u5lemc1b 685 . . . 4 a C ((a5 b) →5 a)
21comcom 453 . . 3 ((a5 b) →5 a) C a
32u5lemc4 705 . 2 (((a5 b) →5 a) →5 a) = (((a5 b) →5 a)a)
4 u5lem1n 743 . . . 4 ((a5 b) →5 a) = ((ab) ∪ (ab ))
54ax-r5 38 . . 3 (((a5 b) →5 a)a) = (((ab) ∪ (ab )) ∪ a)
6 ax-a2 31 . . 3 (((ab) ∪ (ab )) ∪ a) = (a ∪ ((ab) ∪ (ab )))
75, 6ax-r2 36 . 2 (((a5 b) →5 a)a) = (a ∪ ((ab) ∪ (ab )))
83, 7ax-r2 36 1 (((a5 b) →5 a) →5 a) = (a ∪ ((ab) ∪ (ab )))
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →5 wi5 16 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-i5 48  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator