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

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

This axiom is referenced by:  axlttri  9677