Theorem xreqled

Description: Equality implies 'less than or equal to'. (Contributed by Glauco Siliprandi, 17-Aug-2020)

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

Proof

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