Theorem ska6 234

Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA6. (Contributed by NM, 30-Aug-1997.)

Assertion

Ref	Expression
ska6	((a ∩ (b ∩ c)) ≡ ((a ∩ b) ∩ c)) = 1

Proof of Theorem ska6

Step	Hyp	Ref	Expression
1		anass 76	. . 3 ((a ∩ b) ∩ c) = (a ∩ (b ∩ c))
2	1	ax-r1 35	. 2 (a ∩ (b ∩ c)) = ((a ∩ b) ∩ c)
3	2	bi1 118	1 ((a ∩ (b ∩ c)) ≡ ((a ∩ b) ∩ c)) = 1

Syntax hints:   = wb 1   ≡ tb 5   ∩ wa 7  1wt 8

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  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: (None)