Theorem gt0ne0d

Description: Positive implies nonzero. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	gt0ne0d.1	$$⊢\phi \to 0<A$$
Assertion	gt0ne0d	$$⊢\phi \to A\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		gt0ne0d.1	$$⊢\phi \to 0<A$$
2		0red	$$⊢\phi \to 0\in ℝ$$
3	2 1	gtned	$$⊢\phi \to A\ne 0$$