Metamath Proof Explorer

Theorem znegcld

Description: Closure law for negative integers. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis zred.1 
|- ( ph -> A e. ZZ )
Assertion znegcld 
|- ( ph -> -u A e. ZZ )

Proof

Step Hyp Ref Expression
1 zred.1 
 |-  ( ph -> A e. ZZ )
2 znegcl 
 |-  ( A e. ZZ -> -u A e. ZZ )
3 1 2 syl 
 |-  ( ph -> -u A e. ZZ )