Description: Closure for a numeral (with units place). (Contributed by Mario Carneiro, 18-Feb-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | numnncl.1 | |- T e. NN0 |
|
numnncl.2 | |- A e. NN0 |
||
numnncl.3 | |- B e. NN |
||
Assertion | numnncl | |- ( ( T x. A ) + B ) e. NN |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | numnncl.1 | |- T e. NN0 |
|
2 | numnncl.2 | |- A e. NN0 |
|
3 | numnncl.3 | |- B e. NN |
|
4 | 1 2 | nn0mulcli | |- ( T x. A ) e. NN0 |
5 | nn0nnaddcl | |- ( ( ( T x. A ) e. NN0 /\ B e. NN ) -> ( ( T x. A ) + B ) e. NN ) |
|
6 | 4 3 5 | mp2an | |- ( ( T x. A ) + B ) e. NN |