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Axiom ax-pre-apti 6778
Description: Apartness of reals is tight. Axiom for real and complex numbers, justified by theorem axpre-apti 6749. (Contributed by Jim Kingdon, 29-Jan-2020.)
Assertion
Ref Expression
ax-pre-apti  RR  RR  <RR  <RR

Detailed syntax breakdown of Axiom ax-pre-apti
StepHypRef Expression
1 cA . . . 4
2 cr 6690 . . . 4  RR
31, 2wcel 1390 . . 3  RR
4 cB . . . 4
54, 2wcel 1390 . . 3  RR
6 cltrr 6695 . . . . . 6  <RR
71, 4, 6wbr 3755 . . . . 5  <RR
84, 1, 6wbr 3755 . . . . 5  <RR
97, 8wo 628 . . . 4  <RR  <RR
109wn 3 . . 3  <RR  <RR
113, 5, 10w3a 884 . 2  RR  RR  <RR  <RR
121, 4wceq 1242 . 2
1311, 12wi 4 1  RR  RR  <RR  <RR
Colors of variables: wff set class
This axiom is referenced by:  axapti  6867
  Copyright terms: Public domain W3C validator