Theorem leid

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

	Ref	Expression
Assertion	leid	⊢ ( 𝐴 ∈ ℝ → 𝐴 ≤ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐴 = 𝐴
2	1	olci	⊢ ( 𝐴 < 𝐴 ∨ 𝐴 = 𝐴 )
3		leloe	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐴 ∈ ℝ ) → ( 𝐴 ≤ 𝐴 ↔ ( 𝐴 < 𝐴 ∨ 𝐴 = 𝐴 ) ) )
4	2 3	mpbiri	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐴 ∈ ℝ ) → 𝐴 ≤ 𝐴 )
5	4	anidms	⊢ ( 𝐴 ∈ ℝ → 𝐴 ≤ 𝐴 )