Metamath Proof Explorer


Theorem leidd

Description: 'Less than or equal to' is reflexive. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis leidd.1 ⊢ φ → A ∈ ℝ
Assertion leidd ⊢ φ → A ≤ A

Proof

Step Hyp Ref Expression
1 leidd.1 ⊢ φ → A ∈ ℝ
2 leid ⊢ A ∈ ℝ → A ≤ A
3 1 2 syl ⊢ φ → A ≤ A