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Mirrors > Home > MPE Home > Th. List > df-ltxr | Structured version Visualization version Unicode version |
Description: Define 'less than' on the set of extended reals. Definition 12-3.1 of [Gleason] p. 173. Note that in our postulates for complex numbers, is primitive and not necessarily a relation on . (Contributed by NM, 13-Oct-2005.) |
Ref | Expression |
---|---|
df-ltxr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clt 10074 | . 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 | cltrr 9940 | . . . . . 6 | |
10 | 3, 7, 9 | wbr 4653 | . . . . 5 |
11 | 5, 8, 10 | w3a 1037 | . . . 4 |
12 | 11, 2, 6 | copab 4712 | . . 3 |
13 | cmnf 10072 | . . . . . . 7 | |
14 | 13 | csn 4177 | . . . . . 6 |
15 | 4, 14 | cun 3572 | . . . . 5 |
16 | cpnf 10071 | . . . . . 6 | |
17 | 16 | csn 4177 | . . . . 5 |
18 | 15, 17 | cxp 5112 | . . . 4 |
19 | 14, 4 | cxp 5112 | . . . 4 |
20 | 18, 19 | cun 3572 | . . 3 |
21 | 12, 20 | cun 3572 | . 2 |
22 | 1, 21 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: ltrelxr 10099 ltxrlt 10108 ltxr 11949 |
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