Theorem leid

Description: 'Less than or equal to' is reflexive. (Contributed by NM, 18-Aug-1999)

	Ref	Expression
Assertion	leid	$$⊢A\in ℝ\to A\le A$$

Proof

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