Theorem int-eqineqd

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

	Ref	Expression
Hypotheses	int-eqineqd.1	⊢ ( 𝜑 → 𝐵 ∈ ℝ )
	int-eqineqd.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	int-eqineqd	⊢ ( 𝜑 → 𝐵 ≤ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		int-eqineqd.1	⊢ ( 𝜑 → 𝐵 ∈ ℝ )
2		int-eqineqd.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
3	2	eqcomd	⊢ ( 𝜑 → 𝐵 = 𝐴 )
4	1 3	eqled	⊢ ( 𝜑 → 𝐵 ≤ 𝐴 )