QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  u1lemnona GIF version

Theorem u1lemnona 665
Description: Lemma for Sasaki implication study. (Contributed by NM, 16-Dec-1997.)
Assertion
Ref Expression
u1lemnona ((a1 b)a ) = (ab )

Proof of Theorem u1lemnona
StepHypRef Expression
1 u1lemaa 600 . . 3 ((a1 b) ∩ a) = (ab)
2 df-a 40 . . 3 ((a1 b) ∩ a) = ((a1 b)a )
3 df-a 40 . . 3 (ab) = (ab )
41, 2, 33tr2 64 . 2 ((a1 b)a ) = (ab )
54con1 66 1 ((a1 b)a ) = (ab )
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  wa 7  1 wi1 12
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-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator