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Axiom ax-pre-ltirr 7378
Description: Real number less-than is irreflexive. Axiom for real and complex numbers, justified by theorem ax-pre-ltirr 7378. (Contributed by Jim Kingdon, 12-Jan-2020.)
Assertion
Ref Expression
ax-pre-ltirr (𝐴 ∈ ℝ → ¬ 𝐴 < 𝐴)

Detailed syntax breakdown of Axiom ax-pre-ltirr
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cr 7270 . . 3 class
31, 2wcel 1436 . 2 wff 𝐴 ∈ ℝ
4 cltrr 7275 . . . 4 class <
51, 1, 4wbr 3814 . . 3 wff 𝐴 < 𝐴
65wn 3 . 2 wff ¬ 𝐴 < 𝐴
73, 6wi 4 1 wff (𝐴 ∈ ℝ → ¬ 𝐴 < 𝐴)
Colors of variables: wff set class
This axiom is referenced by:  axltirr  7474
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