Theorem id5id0 352

Description: Show that classical identity follows from quantum identity in OL. (Contributed by NM, 4-Mar-2006.)

Hypothesis

Ref	Expression
id5id0.1	(a ≡ b) = 1

Assertion

Ref	Expression
id5id0	(a ≡0 b) = 1

Proof of Theorem id5id0

Step	Hyp	Ref	Expression
1		id5id0.1	. 2 (a ≡ b) = 1
2		id5leid0 351	. . 3 (a ≡ b) ≤ (a ≡0 b)
3	2	sklem 230	. 2 ((a ≡ b)⊥ ∪ (a ≡0 b)) = 1
4	1, 3	skr0 242	1 (a ≡0 b) = 1

Syntax hints:   = wb 1   ≡ tb 5  1wt 8   ≡₀ wid0 17

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  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  df-id0 49  df-le1 130  df-le2 131

This theorem is referenced by:  wdka4o  1116  wddi-0  1117