Theorem nomb32 300

Description: Lemma for "Non-Orthomodular Models..." paper.

Assertion

Ref	Expression
nomb32	(a ==3 b) = (b ==2 a)

Proof of Theorem nomb32

Step	Hyp	Ref	Expression
1		ax-a2 31	. . 3 (a' v b) = (b v a')
2		ancom 74	. . . 4 (a' ^ b') = (b' ^ a')
3	2	lor 70	. . 3 (a v (a' ^ b')) = (a v (b' ^ a'))
4	1, 3	2an 79	. 2 ((a' v b) ^ (a v (a' ^ b'))) = ((b v a') ^ (a v (b' ^ a')))
5		df-id3 52	. 2 (a ==3 b) = ((a' v b) ^ (a v (a' ^ b')))
6		df-id2 51	. 2 (b ==2 a) = ((b v a') ^ (a v (b' ^ a')))
7	4, 5, 6	3tr1 63	1 (a ==3 b) = (b ==2 a)

Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ==2 wid2 19   ==3 wid3 20

This theorem is referenced by:  nomcon3 304  nomcon4 305  nom32 321  nom33 322  nom62 339  nom63 340

This theorem was proved from axioms:  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-id2 51  df-id3 52

Copyright terms: Public domain