Theorem nltled

Description: 'Not less than ' implies 'less than or equal to'. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	ltd.1	$$⊢\phi \to A\in ℝ$$
	ltd.2	$$⊢\phi \to B\in ℝ$$
	nltled.1	$$⊢\phi \to \neg B<A$$
Assertion	nltled	$$⊢\phi \to A\le B$$

Proof

Step	Hyp	Ref	Expression
1		ltd.1	$$⊢\phi \to A\in ℝ$$
2		ltd.2	$$⊢\phi \to B\in ℝ$$
3		nltled.1	$$⊢\phi \to \neg B<A$$
4	1 2	lenltd	$$⊢\phi \to \left(A\le B\leftrightarrow \neg B<A\right)$$
5	3 4	mpbird	$$⊢\phi \to A\le B$$