Theorem 1nuz2

Description: 1 is not in ( ZZ>=2 ) . (Contributed by Paul Chapman, 21-Nov-2012)

	Ref	Expression
Assertion	1nuz2	⊢ ¬ 1 ∈ ( ℤ≥ ‘ 2 )

Proof

Step	Hyp	Ref	Expression
1		neirr	⊢ ¬ 1 ≠ 1
2		eluz2b3	⊢ ( 1 ∈ ( ℤ≥ ‘ 2 ) ↔ ( 1 ∈ ℕ ∧ 1 ≠ 1 ) )
3	2	simprbi	⊢ ( 1 ∈ ( ℤ≥ ‘ 2 ) → 1 ≠ 1 )
4	1 3	mto	⊢ ¬ 1 ∈ ( ℤ≥ ‘ 2 )