Theorem reflcl

Description: The floor (greatest integer) function is real. (Contributed by NM, 15-Jul-2008)

	Ref	Expression
Assertion	reflcl	⊢ ( 𝐴 ∈ ℝ → ( ⌊ ‘ 𝐴 ) ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		flcl	⊢ ( 𝐴 ∈ ℝ → ( ⌊ ‘ 𝐴 ) ∈ ℤ )
2	1	zred	⊢ ( 𝐴 ∈ ℝ → ( ⌊ ‘ 𝐴 ) ∈ ℝ )