Theorem rphalfltd

Description: Half of a positive real is less than the original number. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	rphalfltd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
Assertion	rphalfltd	⊢ ( 𝜑 → ( 𝐴 / 2 ) < 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		rphalfltd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
2		rphalflt	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 / 2 ) < 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 / 2 ) < 𝐴 )