Definition df-id4 52

Description: Define asymmetrical identity (for "Non-Orthomodular Models..." paper).

Assertion

Ref	Expression
df-id4	(a ≡4 b) = ((a⊥ ∪ b) ∩ (b⊥ ∪ (a ∩ b)))

Detailed syntax breakdown of Definition df-id4

Step	Hyp	Ref	Expression
1		wva	. . 3 term  a
2		wvb	. . 3 term  b
3	1, 2	wid4 22	. 2 term  (a ≡4 b)
4	1	wn 4	. . . 4 term  a⊥
5	4, 2	wo 6	. . 3 term  (a⊥ ∪ b)
6	2	wn 4	. . . 4 term  b⊥
7	1, 2	wa 7	. . . 4 term  (a ∩ b)
8	6, 7	wo 6	. . 3 term  (b⊥ ∪ (a ∩ b))
9	5, 8	wa 7	. 2 term  ((a⊥ ∪ b) ∩ (b⊥ ∪ (a ∩ b)))
10	3, 9	wb 1	1 wff  (a ≡4 b) = ((a⊥ ∪ b) ∩ (b⊥ ∪ (a ∩ b)))

This definition is referenced by:  nomb41 291  nom24 309  nom53 326

metamath.org