Metamath Proof Explorer


Theorem mnfltd

Description: Minus infinity is less than any (finite) real. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Hypothesis mnfltd.a ( 𝜑𝐴 ∈ ℝ )
Assertion mnfltd ( 𝜑 → -∞ < 𝐴 )

Proof

Step Hyp Ref Expression
1 mnfltd.a ( 𝜑𝐴 ∈ ℝ )
2 mnflt ( 𝐴 ∈ ℝ → -∞ < 𝐴 )
3 1 2 syl ( 𝜑 → -∞ < 𝐴 )