Theorem xrleid

Description: 'Less than or equal to' is reflexive for extended reals. (Contributed by NM, 7-Feb-2007)

	Ref	Expression
Assertion	xrleid	$$⊢A\in {ℝ}^{*}\to A\le A$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢A=A$$
2	1	olci	$$⊢\left(A<A\vee A=A\right)$$
3		xrleloe	$$⊢\left(A\in {ℝ}^{*}\wedge A\in {ℝ}^{*}\right)\to \left(A\le A\leftrightarrow \left(A<A\vee A=A\right)\right)$$
4	2 3	mpbiri	$$⊢\left(A\in {ℝ}^{*}\wedge A\in {ℝ}^{*}\right)\to A\le A$$
5	4	anidms	$$⊢A\in {ℝ}^{*}\to A\le A$$