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Axiom ax-pre-ltwlin 6796
Description: Real number less-than is weakly linear. Axiom for real and complex numbers, justified by theorem axpre-ltwlin 6767. (Contributed by Jim Kingdon, 12-Jan-2020.)
Assertion
Ref Expression
ax-pre-ltwlin  RR  RR  C  RR  <RR  <RR  C  C  <RR

Detailed syntax breakdown of Axiom ax-pre-ltwlin
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 . . . 4  <RR
101, 4, 9wbr 3755 . . 3  <RR
111, 6, 9wbr 3755 . . . 4  <RR  C
126, 4, 9wbr 3755 . . . 4  C  <RR
1311, 12wo 628 . . 3  <RR  C  C  <RR
1410, 13wi 4 . 2  <RR  <RR  C  C  <RR
158, 14wi 4 1  RR  RR  C  RR  <RR  <RR  C  C  <RR
Colors of variables: wff set class
This axiom is referenced by:  axltwlin  6884
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