MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-pre-lttri Unicode version

Axiom ax-pre-lttri 9587
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.)
Assertion
Ref Expression
ax-pre-lttri

Detailed syntax breakdown of Axiom ax-pre-lttri
StepHypRef Expression
1 cA . . . 4
2 cr 9512 . . . 4
31, 2wcel 1818 . . 3
4 cB . . . 4
54, 2wcel 1818 . . 3
63, 5wa 369 . 2
7 cltrr 9517 . . . 4
81, 4, 7wbr 4452 . . 3
91, 4wceq 1395 . . . . 5
104, 1, 7wbr 4452 . . . . 5
119, 10wo 368 . . . 4
1211wn 3 . . 3
138, 12wb 184 . 2
146, 13wi 4 1
Colors of variables: wff setvar class
This axiom is referenced by:  axlttri  9677
  Copyright terms: Public domain W3C validator