Axiom ax-pre-ltirr 7886

Description: Real number less-than is irreflexive. Axiom for real and complex numbers, justified by Theorem ax-pre-ltirr 7886. (Contributed by Jim Kingdon, 12-Jan-2020.)

Assertion

Ref	Expression
ax-pre-ltirr	⊢ (𝐴 ∈ ℝ → ¬ 𝐴 <ℝ 𝐴)

Detailed syntax breakdown of Axiom ax-pre-ltirr

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cr 7773	. . 3 class ℝ
3	1, 2	wcel 2141	. 2 wff 𝐴 ∈ ℝ
4		cltrr 7778	. . . 4 class <ℝ
5	1, 1, 4	wbr 3989	. . 3 wff 𝐴 <ℝ 𝐴
6	5	wn 3	. 2 wff ¬ 𝐴 <ℝ 𝐴
7	3, 6	wi 4	1 wff (𝐴 ∈ ℝ → ¬ 𝐴 <ℝ 𝐴)

This axiom is referenced by:  axltirr  7986