Theorem num0h

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

	Ref	Expression
Hypotheses	numnncl.1	|- T e. NN0
	numnncl.2	|- A e. NN0
Assertion	num0h	|- A = ( ( T x. 0 ) + A )

Proof

Step	Hyp	Ref	Expression
1		numnncl.1	|- T e. NN0
2		numnncl.2	|- A e. NN0
3	1	nn0cni	|- T e. CC
4	3	mul01i	|- ( T x. 0 ) = 0
5	4	oveq1i	|- ( ( T x. 0 ) + A ) = ( 0 + A )
6	2	nn0cni	|- A e. CC
7	6	addlidi	|- ( 0 + A ) = A
8	5 7	eqtr2i	|- A = ( ( T x. 0 ) + A )