Theorem nomb41 299

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

Assertion

Ref	Expression
nomb41	(a ==4 b) = (b ==1 a)

Proof of Theorem nomb41

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 (b' v (a ^ b)) = (b' v (b ^ a))
4	1, 3	2an 79	. 2 ((a' v b) ^ (b' v (a ^ b))) = ((b v a') ^ (b' v (b ^ a)))
5		df-id4 53	. 2 (a ==4 b) = ((a' v b) ^ (b' v (a ^ b)))
6		df-id1 50	. 2 (b ==1 a) = ((b v a') ^ (b' v (b ^ a)))
7	4, 5, 6	3tr1 63	1 (a ==4 b) = (b ==1 a)

Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ==1 wid1 18   ==4 wid4 21

This theorem is referenced by:  nomcon3 304  nomcon4 305  nom31 320  nom34 323  nom61 338  nom64 341

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-id1 50  df-id4 53

Copyright terms: Public domain