Metamath Proof Explorer


Theorem lem1d

Description: A number minus 1 is less than or equal to itself. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis ltp1d.1 ⊢ φ → A ∈ ℝ
Assertion lem1d ⊢ φ → A − 1 ≤ A

Proof

Step Hyp Ref Expression
1 ltp1d.1 ⊢ φ → A ∈ ℝ
2 lem1 ⊢ A ∈ ℝ → A − 1 ≤ A
3 1 2 syl ⊢ φ → A − 1 ≤ A