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Axiom ax-pre-lttri 9302
Description: Ordering on reals satisfies strict trichotomy. Axiom 18 of 22 for real and complex numbers, justified by theorem axpre-lttri 9278. Note: The more general version for extended reals is axlttri 9392. Normally new proofs would use xrlttri 11061. (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 9227 . . . 4
31, 2wcel 1749 . . 3
4 cB . . . 4
54, 2wcel 1749 . . 3
63, 5wa 362 . 2
7 cltrr 9232 . . . 4
81, 4, 7wbr 4267 . . 3
91, 4wceq 1687 . . . . 5
104, 1, 7wbr 4267 . . . . 5
119, 10wo 361 . . . 4
1211wn 3 . . 3
138, 12wb 178 . 2
146, 13wi 4 1
Colors of variables: wff setvar class
This axiom is referenced by:  axlttri  9392
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