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Axiom ax-pre-lttrn 9303
Description: Ordering on reals is transitive. Axiom 19 of 22 for real and complex numbers, justified by theorem axpre-lttrn 9279. Note: The more general version for extended reals is axlttrn 9393. Normally new proofs would use lttr 9397. (New usage is discouraged.) (Contributed by NM, 13-Oct-2005.)
Assertion
Ref Expression
ax-pre-lttrn

Detailed syntax breakdown of Axiom ax-pre-lttrn
StepHypRef Expression
1 cA . . . 4
2 cr 9227 . . . 4
31, 2wcel 1749 . . 3
4 cB . . . 4
54, 2wcel 1749 . . 3
6 cC . . . 4
76, 2wcel 1749 . . 3
83, 5, 7w3a 950 . 2
9 cltrr 9232 . . . . 5
101, 4, 9wbr 4267 . . . 4
114, 6, 9wbr 4267 . . . 4
1210, 11wa 362 . . 3
131, 6, 9wbr 4267 . . 3
1412, 13wi 4 . 2
158, 14wi 4 1
Colors of variables: wff setvar class
This axiom is referenced by:  axlttrn  9393
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