Metamath Proof Explorer

Theorem zsqcl

Description: Integers are closed under squaring. (Contributed by Scott Fenton, 18-Apr-2014) (Revised by Mario Carneiro, 19-Apr-2014)

Ref Expression
Assertion zsqcl 
|- ( A e. ZZ -> ( A ^ 2 ) e. ZZ )

Proof

Step Hyp Ref Expression
1 2nn0 
 |-  2 e. NN0
2 zexpcl 
 |-  ( ( A e. ZZ /\ 2 e. NN0 ) -> ( A ^ 2 ) e. ZZ )
3 1 2 mpan2 
 |-  ( A e. ZZ -> ( A ^ 2 ) e. ZZ )