QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  ax-3oa Unicode version
Axiom ax-3oa 998
Description: 3-variable consequence of the orthoarguesion law.
Assertion
Ref Expression
ax-3oa ((a ->1 c) ^ ((a ^ b) v ((a ->1 c) ^ (b ->1 c)))) =< (b ->1 c)
Detailed syntax breakdown of Axiom ax-3oa
StepHypRef Expression
1 wva . . . 4 term a
2 wvc . . . 4 term c
31, 2wi1 12 . . 3 term (a ->1 c)
4 wvb . . . . 5 term b
51, 4wa 7 . . . 4 term (a ^ b)
64, 2wi1 12 . . . . 5 term (b ->1 c)
73, 6wa 7 . . . 4 term ((a ->1 c) ^ (b ->1 c))
85, 7wo 6 . . 3 term ((a ^ b) v ((a ->1 c) ^ (b ->1 c)))
93, 8wa 7 . 2 term ((a ->1 c) ^ ((a ^ b) v ((a ->1 c) ^ (b ->1 c))))
109, 6wle 2 1 wff ((a ->1 c) ^ ((a ^ b) v ((a ->1 c) ^ (b ->1 c)))) =< (b ->1 c)
Colors of variables: term
This axiom is referenced by:  oal2  999  3oa2  1024
  Copyright terms: Public domain W3C validator