Theorem xreqled

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

	Ref	Expression
Hypotheses	xreqled.1	$$⊢\phi \to A\in {ℝ}^{*}$$
	xreqled.2	$$⊢\phi \to A=B$$
Assertion	xreqled	$$⊢\phi \to A\le B$$

Proof

Step	Hyp	Ref	Expression
1		xreqled.1	$$⊢\phi \to A\in {ℝ}^{*}$$
2		xreqled.2	$$⊢\phi \to A=B$$
3		xreqle	$$⊢\left(A\in {ℝ}^{*}\wedge A=B\right)\to A\le B$$
4	1 2 3	syl2anc	$$⊢\phi \to A\le B$$