Theorem oml 427

Description: Orthomodular law. Compare Th. 1 of Pavicic 1987.

Assertion

Ref	Expression
oml	(a ∪ (a⊥ ∩ (a ∪ b))) = (a ∪ b)

Proof of Theorem oml

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	lem3.1 425	1 (a ∪ (a⊥ ∩ (a ∪ b))) = (a ∪ b)

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7

This theorem is referenced by:  omln 428  oml5 431  oml2 433  ud1lem2 543  ud2lem2 546  ud3lem2 553  ud4lem2 564  ud5lem3 576  test 784  2oalem1 807  oas 905  oat 907

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  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41

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