Metamath Proof Explorer


Theorem num0u

Description: Add a zero in the units place. (Contributed by Mario Carneiro, 18-Feb-2014)

Ref Expression
Hypotheses numnncl.1
|- T e. NN0
numnncl.2
|- A e. NN0
Assertion num0u
|- ( T x. A ) = ( ( T x. A ) + 0 )

Proof

Step Hyp Ref Expression
1 numnncl.1
 |-  T e. NN0
2 numnncl.2
 |-  A e. NN0
3 1 2 nn0mulcli
 |-  ( T x. A ) e. NN0
4 3 nn0cni
 |-  ( T x. A ) e. CC
5 4 addid1i
 |-  ( ( T x. A ) + 0 ) = ( T x. A )
6 5 eqcomi
 |-  ( T x. A ) = ( ( T x. A ) + 0 )