Theorem mnfled

Description: Minus infinity is less than or equal to any extended real. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	mnfled.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
Assertion	mnfled	⊢ ( 𝜑 → -∞ ≤ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		mnfled.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
2		mnfle	⊢ ( 𝐴 ∈ ℝ* → -∞ ≤ 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → -∞ ≤ 𝐴 )