Theorem woml 203

Description: Theorem structurally similar to orthomodular law but does not require R3.

Assertion

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

Proof of Theorem woml

Step	Hyp	Ref	Expression
1		omlem1 119	. 2 ((a ∪ (a⊥ ∩ (a ∪ b))) ∪ (a ∪ b)) = (a ∪ b)
2		omlem2 120	. 2 ((a ∪ b)⊥ ∪ (a ∪ (a⊥ ∩ (a ∪ b)))) = 1
3	1, 2	wlem3.1 202	1 ((a ∪ (a⊥ ∩ (a ∪ b))) ≡ (a ∪ b)) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 9

This theorem is referenced by:  wwoml2 204  ska11 231  wom4 362

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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