QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  gstho Unicode version
Theorem gstho 491
Description: "OR" version of Gudder-Schelp's Theorem.
Hypotheses
Ref Expression
gstho.1 b C c
gstho.2 a C (b v c)
Assertion
Ref Expression
gstho (a v b) C c
Proof of Theorem gstho
StepHypRef Expression
1 anor3 90 . . . 4 (a' ^ b') = (a v b)'
21ax-r1 35 . . 3 (a v b)' = (a' ^ b')
3 gstho.1 . . . . 5 b C c
43comcom4 455 . . . 4 b' C c'
5 gstho.2 . . . . . 6 a C (b v c)
65comcom4 455 . . . . 5 a' C (b v c)'
7 anor3 90 . . . . . 6 (b' ^ c') = (b v c)'
87ax-r1 35 . . . . 5 (b v c)' = (b' ^ c')
96, 8cbtr 182 . . . 4 a' C (b' ^ c')
104, 9gsth2 490 . . 3 (a' ^ b') C c'
112, 10bctr 181 . 2 (a v b)' C c'
1211comcom5 458 1 (a v b) C c
Colors of variables: term
Syntax hints:   C wc 3  'wn 4   v wo 6   ^ wa 7
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-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator