Theorem ska5 233

Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA5. (Contributed by NM, 30-Aug-1997.)

Assertion

Ref	Expression
ska5	((a ∩ b) ≡ (b ∩ a)) = 1

Proof of Theorem ska5

Step	Hyp	Ref	Expression
1		ancom 74	. 2 (a ∩ b) = (b ∩ a)
2	1	bi1 118	1 ((a ∩ b) ≡ (b ∩ a)) = 1

Syntax hints:   = wb 1   ≡ tb 5   ∩ 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: (None)