Theorem ska6 226

Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA6.

Assertion

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

Proof of Theorem ska6

Step	Hyp	Ref	Expression
1		anass 69	. . 3 ((a ∩ b) ∩ c) = (a ∩ (b ∩ c))
2	1	ax-r1 34	. 2 (a ∩ (b ∩ c)) = ((a ∩ b) ∩ c)
3	2	bi1 110	1 ((a ∩ (b ∩ c)) ≡ ((a ∩ b) ∩ c)) = 1

Syntax hints:   = wb 1   ≡ tb 5   ∩ wa 7  1wt 9

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41

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