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Axiom ax-pre-lttrn 6797
Description: Ordering on reals is transitive. Axiom for real and complex numbers, justified by theorem axpre-lttrn 6768. (Contributed by NM, 13-Oct-2005.)
Assertion
Ref Expression
ax-pre-lttrn  RR  RR  C  RR  <RR  <RR  C  <RR  C

Detailed syntax breakdown of Axiom ax-pre-lttrn
StepHypRef Expression
1 cA . . . 4
2 cr 6710 . . . 4  RR
31, 2wcel 1390 . . 3  RR
4 cB . . . 4
54, 2wcel 1390 . . 3  RR
6 cC . . . 4  C
76, 2wcel 1390 . . 3  C  RR
83, 5, 7w3a 884 . 2  RR  RR  C  RR
9 cltrr 6715 . . . . 5  <RR
101, 4, 9wbr 3755 . . . 4  <RR
114, 6, 9wbr 3755 . . . 4  <RR  C
1210, 11wa 97 . . 3  <RR  <RR  C
131, 6, 9wbr 3755 . . 3  <RR  C
1412, 13wi 4 . 2  <RR  <RR  C  <RR  C
158, 14wi 4 1  RR  RR  C  RR  <RR  <RR  C  <RR  C
Colors of variables: wff set class
This axiom is referenced by:  axlttrn  6885
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