Metamath Proof Explorer


Theorem numcl

Description: Closure for a decimal integer (with units place). (Contributed by Mario Carneiro, 18-Feb-2014)

Ref Expression
Hypotheses numnncl.1
|- T e. NN0
numnncl.2
|- A e. NN0
numcl.2
|- B e. NN0
Assertion numcl
|- ( ( T x. A ) + B ) e. NN0

Proof

Step Hyp Ref Expression
1 numnncl.1
 |-  T e. NN0
2 numnncl.2
 |-  A e. NN0
3 numcl.2
 |-  B e. NN0
4 1 2 nn0mulcli
 |-  ( T x. A ) e. NN0
5 4 3 nn0addcli
 |-  ( ( T x. A ) + B ) e. NN0