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 e. RR
Assertion	msqgt0i	|- ( A =/= 0 -> 0 < ( A x. A ) )

Proof

Step	Hyp	Ref	Expression
1		lt2.1	|- A e. RR
2		msqgt0	|- ( ( A e. RR /\ A =/= 0 ) -> 0 < ( A x. A ) )
3	1 2	mpan	|- ( A =/= 0 -> 0 < ( A x. A ) )