Theorem rpne0d

Description: A positive real is nonzero. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	rpred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
Assertion	rpne0d	⊢ ( 𝜑 → 𝐴 ≠ 0 )

Proof

Step	Hyp	Ref	Expression
1		rpred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
2		rpne0	⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ≠ 0 )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ≠ 0 )