Theorem oml2 451

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 445	. 2 (a v (a' ^ (a v b))) = (a v b)
2		oml2.1	. . . . 5 a =< b
3	2	df-le2 131	. . . 4 (a v b) = b
4	3	lan 77	. . 3 (a' ^ (a v b)) = (a' ^ b)
5	4	lor 70	. 2 (a v (a' ^ (a v b))) = (a v (a' ^ b))
6	1, 5, 3	3tr2 64	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 452  comcom 453  com3i 467  lem4 511  lem4.6.6i4j2 1098

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  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-le2 131

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