Theorem ska10 238

Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA10. (Contributed by NM, 30-Aug-1997.)

Assertion

Ref	Expression
ska10	((a ∪ b)⊥ ≡ (a⊥ ∩ b⊥ )) = 1

Proof of Theorem ska10

Step	Hyp	Ref	Expression
1		oran 87	. . 3 (a ∪ b) = (a⊥ ∩ b⊥ )⊥
2	1	con2 67	. 2 (a ∪ b)⊥ = (a⊥ ∩ b⊥ )
3	2	bi1 118	1 ((a ∪ b)⊥ ≡ (a⊥ ∩ b⊥ )) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 8

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42

This theorem is referenced by:  ska2  432