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Mirrors > Home > MPE Home > Th. List > df-lt | Structured version Visualization version Unicode version |
Description: Define 'less than' on the real subset of complex numbers. Proofs should typically use instead; see df-ltxr 10079. (Contributed by NM, 22-Feb-1996.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-lt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cltrr 9940 | . 2 | |
2 | vx | . . . . . . 7 | |
3 | 2 | cv 1482 | . . . . . 6 |
4 | cr 9935 | . . . . . 6 | |
5 | 3, 4 | wcel 1990 | . . . . 5 |
6 | vy | . . . . . . 7 | |
7 | 6 | cv 1482 | . . . . . 6 |
8 | 7, 4 | wcel 1990 | . . . . 5 |
9 | 5, 8 | wa 384 | . . . 4 |
10 | vz | . . . . . . . . . . 11 | |
11 | 10 | cv 1482 | . . . . . . . . . 10 |
12 | c0r 9688 | . . . . . . . . . 10 | |
13 | 11, 12 | cop 4183 | . . . . . . . . 9 |
14 | 3, 13 | wceq 1483 | . . . . . . . 8 |
15 | vw | . . . . . . . . . . 11 | |
16 | 15 | cv 1482 | . . . . . . . . . 10 |
17 | 16, 12 | cop 4183 | . . . . . . . . 9 |
18 | 7, 17 | wceq 1483 | . . . . . . . 8 |
19 | 14, 18 | wa 384 | . . . . . . 7 |
20 | cltr 9693 | . . . . . . . 8 | |
21 | 11, 16, 20 | wbr 4653 | . . . . . . 7 |
22 | 19, 21 | wa 384 | . . . . . 6 |
23 | 22, 15 | wex 1704 | . . . . 5 |
24 | 23, 10 | wex 1704 | . . . 4 |
25 | 9, 24 | wa 384 | . . 3 |
26 | 25, 2, 6 | copab 4712 | . 2 |
27 | 1, 26 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: ltrelre 9955 ltresr 9961 |
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