Theorem ska10 230

Description: Soundness theorem for Kalmbach's quantum propositional logic axiom KA10.

Assertion

Ref	Expression
ska10	((a v b)_|_ == (a_|_ ^ b_|_)) = 1

Proof of Theorem ska10

Step	Hyp	Ref	Expression
1		oran 79	. . 3 (a v b) = (a_|_ ^ b_|_)_|_
2	1	con2 64	. 2 (a v b)_|_ = (a_|_ ^ b_|_)
3	2	bi1 110	1 ((a v b)_|_ == (a_|_ ^ b_|_)) = 1

Syntax hints:   = wb 1  _|_wn 4   == tb 5   v wo 6   ^ wa 7  1wt 9

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  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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