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Mirrors > Home > QLE Home > Th. List > df-id4oa | GIF version |
Description: The 4-variable orthoarguesian identity term. (Contributed by NM, 28-Nov-1998.) |
Ref | Expression |
---|---|
df-id4oa | (a ≡ c, d ≡OA b) = ((a ≡ d ≡OA b) ∪ ((a ≡ d ≡OA c) ∩ (b ≡ d ≡OA c))) |
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 28 | . 2 term (a ≡ c, d ≡OA b) |
6 | 1, 2, 4 | wid3oa 27 | . . 3 term (a ≡ d ≡OA b) |
7 | 1, 3, 4 | wid3oa 27 | . . . 4 term (a ≡ d ≡OA c) |
8 | 2, 3, 4 | wid3oa 27 | . . . 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))) |
Colors of variables: term |
This definition is referenced by: (None) |
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