Theorem ceilcld

Description: Closure of the ceiling function. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	ceilcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	ceilcld	⊢ ( 𝜑 → ( ⌈ ‘ 𝐴 ) ∈ ℤ )

Proof

Step	Hyp	Ref	Expression
1		ceilcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		ceilcl	⊢ ( 𝐴 ∈ ℝ → ( ⌈ ‘ 𝐴 ) ∈ ℤ )
3	1 2	syl	⊢ ( 𝜑 → ( ⌈ ‘ 𝐴 ) ∈ ℤ )