Metamath Proof Explorer


Theorem xrleidd

Description: 'Less than or equal to' is reflexive for extended reals. Deduction form of xrleid . (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypothesis xrleidd.1 ⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
Assertion xrleidd ( 𝜑 → 𝐴 ≤ 𝐴 )

Proof

Step Hyp Ref Expression
1 xrleidd.1 ⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
2 xrleid ⊢ ( 𝐴 ∈ ℝ* → 𝐴 ≤ 𝐴 )
3 1 2 syl ⊢ ( 𝜑 → 𝐴 ≤ 𝐴 )