Theorem msqgt0d

Description: A nonzero square is positive. Theorem I.20 of Apostol p. 20. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	leidd.1	$$⊢\phi \to A\in ℝ$$
	msqgt0d.2	$$⊢\phi \to A\ne 0$$
Assertion	msqgt0d	$$⊢\phi \to 0<AA$$

Proof

Step	Hyp	Ref	Expression
1		leidd.1	$$⊢\phi \to A\in ℝ$$
2		msqgt0d.2	$$⊢\phi \to A\ne 0$$
3		msqgt0	$$⊢\left(A\in ℝ\wedge A\ne 0\right)\to 0<AA$$
4	1 2 3	syl2anc	$$⊢\phi \to 0<AA$$