Theorem eluz4eluz2

Description: An integer greater than or equal to 4 is an integer greater than or equal to 2. (Contributed by AV, 30-May-2023)

	Ref	Expression
Assertion	eluz4eluz2	⊢ ( 𝑋 ∈ ( ℤ≥ ‘ 4 ) → 𝑋 ∈ ( ℤ≥ ‘ 2 ) )

Proof

Step	Hyp	Ref	Expression
1		2z	⊢ 2 ∈ ℤ
2		2re	⊢ 2 ∈ ℝ
3		4re	⊢ 4 ∈ ℝ
4		2lt4	⊢ 2 < 4
5	2 3 4	ltleii	⊢ 2 ≤ 4
6		eluzuzle	⊢ ( ( 2 ∈ ℤ ∧ 2 ≤ 4 ) → ( 𝑋 ∈ ( ℤ≥ ‘ 4 ) → 𝑋 ∈ ( ℤ≥ ‘ 2 ) ) )
7	1 5 6	mp2an	⊢ ( 𝑋 ∈ ( ℤ≥ ‘ 4 ) → 𝑋 ∈ ( ℤ≥ ‘ 2 ) )