Metamath Proof Explorer

Theorem sqgt0i

Description: The square of a nonzero real is positive. (Contributed by NM, 17-Sep-1999)

Ref Expression
Hypothesis resqcl.1 
|- A e. RR
Assertion sqgt0i 
|- ( A =/= 0 -> 0 < ( A ^ 2 ) )

Proof

Step Hyp Ref Expression
1 resqcl.1 
 |-  A e. RR
2 sqgt0 
 |-  ( ( A e. RR /\ A =/= 0 ) -> 0 < ( A ^ 2 ) )
3 1 2 mpan 
 |-  ( A =/= 0 -> 0 < ( A ^ 2 ) )