Theorem oml2 433

Description: Orthomodular law. Kalmbach 83 p. 22.

Hypothesis

Ref	Expression
oml2.1	a =< b

Assertion

Ref	Expression
oml2	(a v (a_|_ ^ b)) = b

Proof of Theorem oml2

Step	Hyp	Ref	Expression
1		oml 427	. 2 (a v (a_|_ ^ (a v b))) = (a v b)
2		oml2.1	. . . . 5 a =< b
3	2	df-le2 123	. . . 4 (a v b) = b
4	3	lan 70	. . 3 (a_|_ ^ (a v b)) = (a_|_ ^ b)
5	4	lor 66	. 2 (a v (a_|_ ^ (a v b))) = (a v (a_|_ ^ b))
6	1, 5, 3	3tr2 61	1 (a v (a_|_ ^ b)) = b

Syntax hints:   = wb 1   =< wle 2  _|_wn 4   v wo 6   ^ wa 7

This theorem is referenced by:  oml3 434  comcom 435  com3i 449  lem4 493

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  df-le2 123

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