Theorem int-eqineqd

Description: EquivalenceImpliesDoubleInequality generator rule. (Contributed by Stanislas Polu, 7-Apr-2020)

	Ref	Expression
Hypotheses	int-eqineqd.1	$$⊢\phi \to B\in ℝ$$
	int-eqineqd.2	$$⊢\phi \to A=B$$
Assertion	int-eqineqd	$$⊢\phi \to B\le A$$

Proof

Step	Hyp	Ref	Expression
1		int-eqineqd.1	$$⊢\phi \to B\in ℝ$$
2		int-eqineqd.2	$$⊢\phi \to A=B$$
3	2	eqcomd	$$⊢\phi \to B=A$$
4	1 3	eqled	$$⊢\phi \to B\le A$$