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Mirrors > Home > MPE Home > Th. List > ax-pre-lttri | Unicode version |
Description: Ordering on reals satisfies strict trichotomy. Axiom 18 of 22 for real and complex numbers, justified by theorem axpre-lttri 9563. Note: The more general version for extended reals is axlttri 9677. Normally new proofs would use xrlttri 11374. (New usage is discouraged.) (Contributed by NM, 13-Oct-2005.) |
Ref | Expression |
---|---|
ax-pre-lttri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cr 9512 | . . . 4 | |
3 | 1, 2 | wcel 1818 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 1818 | . . 3 |
6 | 3, 5 | wa 369 | . 2 |
7 | cltrr 9517 | . . . 4 | |
8 | 1, 4, 7 | wbr 4452 | . . 3 |
9 | 1, 4 | wceq 1395 | . . . . 5 |
10 | 4, 1, 7 | wbr 4452 | . . . . 5 |
11 | 9, 10 | wo 368 | . . . 4 |
12 | 11 | wn 3 | . . 3 |
13 | 8, 12 | wb 184 | . 2 |
14 | 6, 13 | wi 4 | 1 |
Colors of variables: wff setvar class |
This axiom is referenced by: axlttri 9677 |
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