Definition df-id4oa 57

Description: The 4-variable orthoarguesian identity term.

Assertion

Ref	Expression
df-id4oa	(a ≡ c, d ≡OA b) = ((a ≡ d ≡OA b) ∪ ((a ≡ d ≡OA c) ∩ (b ≡ d ≡OA c)))

Detailed syntax breakdown of Definition df-id4oa

Step	Hyp	Ref	Expression
1		wva	. . 3 term  a
2		wvb	. . 3 term  b
3		wvc	. . 3 term  c
4		wvd	. . 3 term  d
5	1, 2, 3, 4	wid4oa 27	. 2 term  (a ≡ c, d ≡OA b)
6	1, 2, 4	wid3oa 26	. . 3 term  (a ≡ d ≡OA b)
7	1, 3, 4	wid3oa 26	. . . 4 term  (a ≡ d ≡OA c)
8	2, 3, 4	wid3oa 26	. . . 4 term  (b ≡ d ≡OA c)
9	7, 8	wa 7	. . 3 term  ((a ≡ d ≡OA c) ∩ (b ≡ d ≡OA c))
10	6, 9	wo 6	. 2 term  ((a ≡ d ≡OA b) ∪ ((a ≡ d ≡OA c) ∩ (b ≡ d ≡OA c)))
11	5, 10	wb 1	1 wff  (a ≡ c, d ≡OA b) = ((a ≡ d ≡OA b) ∪ ((a ≡ d ≡OA c) ∩ (b ≡ d ≡OA c)))

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