Theorem ltleii

Description: 'Less than' implies 'less than or equal to' (inference). (Contributed by NM, 22-Aug-1999)

	Ref	Expression
Hypotheses	lt.1	⊢ 𝐴 ∈ ℝ
	lt.2	⊢ 𝐵 ∈ ℝ
	ltlei.1	⊢ 𝐴 < 𝐵
Assertion	ltleii	⊢ 𝐴 ≤ 𝐵

Proof

Step	Hyp	Ref	Expression
1		lt.1	⊢ 𝐴 ∈ ℝ
2		lt.2	⊢ 𝐵 ∈ ℝ
3		ltlei.1	⊢ 𝐴 < 𝐵
4	1 2	ltlei	⊢ ( 𝐴 < 𝐵 → 𝐴 ≤ 𝐵 )
5	3 4	ax-mp	⊢ 𝐴 ≤ 𝐵