Theorem 2eluzge1

Description: 2 is an integer greater than or equal to 1. (Contributed by Alexander van der Vekens, 8-Jun-2018)

	Ref	Expression
Assertion	2eluzge1	⊢ 2 ∈ ( ℤ≥ ‘ 1 )

Proof

Step	Hyp	Ref	Expression
1		1z	⊢ 1 ∈ ℤ
2		2z	⊢ 2 ∈ ℤ
3		1le2	⊢ 1 ≤ 2
4		eluz2	⊢ ( 2 ∈ ( ℤ≥ ‘ 1 ) ↔ ( 1 ∈ ℤ ∧ 2 ∈ ℤ ∧ 1 ≤ 2 ) )
5	1 2 3 4	mpbir3an	⊢ 2 ∈ ( ℤ≥ ‘ 1 )