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 )