This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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 )