Theorem rprene0

Description: A positive real is a nonzero real number. (Contributed by NM, 11-Nov-2008)

	Ref	Expression
Assertion	rprene0	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 ∈ ℝ ∧ 𝐴 ≠ 0 ) )

Proof

Step	Hyp	Ref	Expression
1		rpre	⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ )
2		rpne0	⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ≠ 0 )
3	1 2	jca	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 ∈ ℝ ∧ 𝐴 ≠ 0 ) )