Metamath Proof Explorer

Theorem evendiv2z

Description: The result of dividing an even number by 2 is an integer. (Contributed by AV, 15-Jun-2020)

Ref Expression
Assertion evendiv2z 
|- ( Z e. Even -> ( Z / 2 ) e. ZZ )

Proof

Step Hyp Ref Expression
1 iseven 
 |-  ( Z e. Even <-> ( Z e. ZZ /\ ( Z / 2 ) e. ZZ ) )
2 1 simprbi 
 |-  ( Z e. Even -> ( Z / 2 ) e. ZZ )