Theorem msqgt0i

Description: A nonzero square is positive. Theorem I.20 of Apostol p. 20. (Contributed by NM, 17-Jan-1997) (Revised by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	lt2.1	$$⊢A\in ℝ$$
Assertion	msqgt0i	$$⊢A\ne 0\to 0<AA$$

Proof

Step	Hyp	Ref	Expression
1		lt2.1	$$⊢A\in ℝ$$
2		msqgt0	$$⊢\left(A\in ℝ\wedge A\ne 0\right)\to 0<AA$$
3	1 2	mpan	$$⊢A\ne 0\to 0<AA$$