Theorem uzuzle35

Description: An integer greater than or equal to 5 is an integer greater than or equal to 3. (Contributed by AV, 15-Nov-2025)

	Ref	Expression
Assertion	uzuzle35	⊢ ( 𝐴 ∈ ( ℤ≥ ‘ 5 ) → 𝐴 ∈ ( ℤ≥ ‘ 3 ) )

Proof

Step	Hyp	Ref	Expression
1		5eluz3	⊢ 5 ∈ ( ℤ≥ ‘ 3 )
2		uzss	⊢ ( 5 ∈ ( ℤ≥ ‘ 3 ) → ( ℤ≥ ‘ 5 ) ⊆ ( ℤ≥ ‘ 3 ) )
3	1 2	ax-mp	⊢ ( ℤ≥ ‘ 5 ) ⊆ ( ℤ≥ ‘ 3 )
4	3	sseli	⊢ ( 𝐴 ∈ ( ℤ≥ ‘ 5 ) → 𝐴 ∈ ( ℤ≥ ‘ 3 ) )