Description: Closure of addition of positive integers. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | nnge1d.1 | |- ( ph -> A e. NN ) |
|
nnmulcld.2 | |- ( ph -> B e. NN ) |
||
Assertion | nnaddcld | |- ( ph -> ( A + B ) e. NN ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnge1d.1 | |- ( ph -> A e. NN ) |
|
2 | nnmulcld.2 | |- ( ph -> B e. NN ) |
|
3 | nnaddcl | |- ( ( A e. NN /\ B e. NN ) -> ( A + B ) e. NN ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( A + B ) e. NN ) |