Theorem mnfltd

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

	Ref	Expression
Hypothesis	mnfltd.a	$$⊢\phi \to A\in ℝ$$
Assertion	mnfltd	$$⊢\phi \to \mathrm{-\infty }<A$$

Proof

Step	Hyp	Ref	Expression
1		mnfltd.a	$$⊢\phi \to A\in ℝ$$
2		mnflt	$$⊢A\in ℝ\to \mathrm{-\infty }<A$$
3	1 2	syl	$$⊢\phi \to \mathrm{-\infty }<A$$