Metamath Proof Explorer


Theorem jm2.27dlem3

Description: Lemma for rmydioph . Infer membership of the endpoint of a range. (Contributed by Stefan O'Rear, 11-Oct-2014)

Ref Expression
Hypothesis jm2.27dlem3.1 ⊢ A ∈ ℕ
Assertion jm2.27dlem3 ⊢ A ∈ 1 … A

Proof

Step Hyp Ref Expression
1 jm2.27dlem3.1 ⊢ A ∈ ℕ
2 elfz1end ⊢ A ∈ ℕ ↔ A ∈ 1 … A
3 1 2 mpbi ⊢ A ∈ 1 … A