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Axiom ax-pre-ltirr 7053
Description: Real number less-than is irreflexive. Axiom for real and complex numbers, justified by theorem ax-pre-ltirr 7053. (Contributed by Jim Kingdon, 12-Jan-2020.)
Assertion
Ref Expression
ax-pre-ltirr  |-  ( A  e.  RR  ->  -.  A  <RR  A )

Detailed syntax breakdown of Axiom ax-pre-ltirr
StepHypRef Expression
1 cA . . 3  class  A
2 cr 6945 . . 3  class  RR
31, 2wcel 1409 . 2  wff  A  e.  RR
4 cltrr 6950 . . . 4  class  <RR
51, 1, 4wbr 3791 . . 3  wff  A  <RR  A
65wn 3 . 2  wff  -.  A  <RR  A
73, 6wi 4 1  wff  ( A  e.  RR  ->  -.  A  <RR  A )
Colors of variables: wff set class
This axiom is referenced by:  axltirr  7144
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