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Axiom ax-pre-ltadd 6759
Description: Ordering property of addition on reals. Axiom for real and complex numbers, justified by theorem axpre-ltadd 6730. (Contributed by NM, 13-Oct-2005.)
Assertion
Ref Expression
ax-pre-ltadd  RR  RR  C  RR  <RR  C  +  <RR  C  +

Detailed syntax breakdown of Axiom ax-pre-ltadd
StepHypRef Expression
1 cA . . . 4
2 cr 6670 . . . 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 6675 . . . 4  <RR
101, 4, 9wbr 3755 . . 3  <RR
11 caddc 6674 . . . . 5  +
126, 1, 11co 5455 . . . 4  C  +
136, 4, 11co 5455 . . . 4  C  +
1412, 13, 9wbr 3755 . . 3  C  +  <RR  C  +
1510, 14wi 4 . 2  <RR  C  +  <RR  C  +
168, 15wi 4 1  RR  RR  C  RR  <RR  C  +  <RR  C  +
Colors of variables: wff set class
This axiom is referenced by:  axltadd  6846
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