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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 ⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion mnfltd ( 𝜑 → -∞ < 𝐴 )

Proof

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