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Metamath Proof Explorer

Theorem mnfled

Description: Minus infinity is less than or equal to any extended real. (Contributed by Glauco Siliprandi, 26-Jun-2021)

		Ref	Expression
	Hypothesis	mnfled.1	$⊢ φ \to A \in ℝ^{*}$
	Assertion	mnfled	$⊢ φ \to −∞ \leq A$

Step	Hyp	Ref	Expression
1		mnfled.1	$⊢ φ \to A \in ℝ^{*}$
2		mnfle	$⊢ A \in ℝ^{*} \to −∞ \leq A$
3	1 2	syl	$⊢ φ \to −∞ \leq A$