Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  u1lemc1 GIF version

Theorem u1lemc1 680
 Description: Commutation theorem for Sasaki implication.
Assertion
Ref Expression
u1lemc1 a C (a1 b)

Proof of Theorem u1lemc1
StepHypRef Expression
1 comid 187 . . . 4 a C a
21comcom2 183 . . 3 a C a
3 comanr1 464 . . 3 a C (ab)
42, 3com2or 483 . 2 a C (a ∪ (ab))
5 df-i1 44 . . 3 (a1 b) = (a ∪ (ab))
65ax-r1 35 . 2 (a ∪ (ab)) = (a1 b)
74, 6cbtr 182 1 a C (a1 b)
 Colors of variables: term Syntax hints:   C wc 3  ⊥ 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:  u1lemc5  696  u12lembi  726  u1lem1  734  u1lem4  757  oas  925  oau  929
 Copyright terms: Public domain W3C validator