Theorem woml 211

Description: Theorem structurally similar to orthomodular law but does not require R3. (Contributed by NM, 2-Sep-1997.)

Assertion

Ref	Expression
woml	((a ∪ (a⊥ ∩ (a ∪ b))) ≡ (a ∪ b)) = 1

Proof of Theorem woml

Step	Hyp	Ref	Expression
1		omlem1 127	. 2 ((a ∪ (a⊥ ∩ (a ∪ b))) ∪ (a ∪ b)) = (a ∪ b)
2		omlem2 128	. 2 ((a ∪ b)⊥ ∪ (a ∪ (a⊥ ∩ (a ∪ b)))) = 1
3	1, 2	wlem3.1 210	1 ((a ∪ (a⊥ ∩ (a ∪ b))) ≡ (a ∪ b)) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ 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:  wwoml2  212  ska11  239  wom4  380