Theorem rpne0d

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

	Ref	Expression
Hypothesis	rpred.1	$$⊢\phi \to A\in {ℝ}^{+}$$
Assertion	rpne0d	$$⊢\phi \to A\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		rpred.1	$$⊢\phi \to A\in {ℝ}^{+}$$
2		rpne0	$$⊢A\in {ℝ}^{+}\to A\ne 0$$
3	1 2	syl	$$⊢\phi \to A\ne 0$$