Theorem eqled

Description: Equality implies 'less than or equal to'. (Contributed by Glauco Siliprandi, 11-Dec-2019)

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

Proof

Step	Hyp	Ref	Expression
1		eqled.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		eqled.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
3		eqle	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐴 = 𝐵 ) → 𝐴 ≤ 𝐵 )
4	1 2 3	syl2anc	⊢ ( 𝜑 → 𝐴 ≤ 𝐵 )