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