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Mirrors > Home > QLE Home > Th. List > df-cmtr | GIF version |
Description: Define "commutator". (Contributed by NM, 24-Jan-1999.) |
Ref | Expression |
---|---|
df-cmtr | C (a, b) = (((a ∩ b) ∪ (a ∩ b⊥ )) ∪ ((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wva | . . 3 term a | |
2 | wvb | . . 3 term b | |
3 | 1, 2 | wcmtr 29 | . 2 term C (a, b) |
4 | 1, 2 | wa 7 | . . . 4 term (a ∩ b) |
5 | 2 | wn 4 | . . . . 5 term b⊥ |
6 | 1, 5 | wa 7 | . . . 4 term (a ∩ b⊥ ) |
7 | 4, 6 | wo 6 | . . 3 term ((a ∩ b) ∪ (a ∩ b⊥ )) |
8 | 1 | wn 4 | . . . . 5 term a⊥ |
9 | 8, 2 | wa 7 | . . . 4 term (a⊥ ∩ b) |
10 | 8, 5 | wa 7 | . . . 4 term (a⊥ ∩ b⊥ ) |
11 | 9, 10 | wo 6 | . . 3 term ((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) |
12 | 7, 11 | wo 6 | . 2 term (((a ∩ b) ∪ (a ∩ b⊥ )) ∪ ((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ ))) |
13 | 3, 12 | wb 1 | 1 wff C (a, b) = (((a ∩ b) ∪ (a ∩ b⊥ )) ∪ ((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ ))) |
Colors of variables: term |
This definition is referenced by: cmtrcom 190 wdf-c1 383 wdf-c2 384 cmtr1com 493 comcmtr1 494 i0cmtrcom 495 3vded22 818 wdcom 1105 wdwom 1106 |
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