Theorem nomb41 291

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 30	. . 3 (a_|_ v b) = (b v a_|_)
2		ancom 68	. . . 4 (a ^ b) = (b ^ a)
3	2	lor 66	. . 3 (b_|_ v (a ^ b)) = (b_|_ v (b ^ a))
4	1, 3	2an 72	. 2 ((a_|_ v b) ^ (b_|_ v (a ^ b))) = ((b v a_|_) ^ (b_|_ v (b ^ a)))
5		df-id4 52	. 2 (a ==4 b) = ((a_|_ v b) ^ (b_|_ v (a ^ b)))
6		df-id1 49	. 2 (b ==1 a) = ((b v a_|_) ^ (b_|_ v (b ^ a)))
7	4, 5, 6	3tr1 60	1 (a ==4 b) = (b ==1 a)

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ==1 wid1 19   ==4 wid4 22

This theorem is referenced by:  nomcon3 296  nomcon4 297  nom31 312  nom34 315  nom61 330  nom64 333

This theorem was proved from axioms:  ax-a2 30  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-id1 49  df-id4 52

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