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Metamath Proof Explorer

Theorem lerelxr

Description: "Less than or equal to" is a relation on extended reals. (Contributed by Mario Carneiro, 28-Apr-2015)

		Ref	Expression
	Assertion	lerelxr	$⊢ \leq \subseteq ℝ^{} \times ℝ^{}$

Step	Hyp	Ref	Expression
1		df-le	$⊢ \leq = (ℝ^{} \times ℝ^{}) ∖ <^{-1}$
2		difss	$⊢ (ℝ^{} \times ℝ^{}) ∖ <^{-1} \subseteq ℝ^{} \times ℝ^{}$
3	1 2	eqsstri	$⊢ \leq \subseteq ℝ^{} \times ℝ^{}$