Theorem sqgt0d

Description: The square of a nonzero real is positive. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	sqgt0d.1	|- ( ph -> A e. RR )
	sqgt0d.2	|- ( ph -> A =/= 0 )
Assertion	sqgt0d	|- ( ph -> 0 < ( A ^ 2 ) )

Proof

Step	Hyp	Ref	Expression
1		sqgt0d.1	|- ( ph -> A e. RR )
2		sqgt0d.2	|- ( ph -> A =/= 0 )
3		sqgt0	|- ( ( A e. RR /\ A =/= 0 ) -> 0 < ( A ^ 2 ) )
4	1 2 3	syl2anc	|- ( ph -> 0 < ( A ^ 2 ) )