Theorem addid2i 8164

Description: 0 is a left identity for addition. (Contributed by NM, 3-Jan-2013.)

Hypothesis

Ref	Expression
mul.1	|- A e. CC

Assertion

Ref	Expression
addid2i	|- ( 0 + A ) = A

Proof of Theorem addid2i

Step	Hyp	Ref	Expression
1		mul.1	. 2 |- A e. CC
2		addlid 8160	. 2 |- ( A e. CC -> ( 0 + A ) = A )
3	1, 2	ax-mp 5	1 |- ( 0 + A ) = A

Syntax hints:   = wceq 1364   e. wcel 2164  (class class class)co 5919   CCcc 7872   0cc0 7874   + caddc 7877

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2175  ax-1cn 7967  ax-icn 7969  ax-addcl 7970  ax-mulcl 7972  ax-addcom 7974  ax-i2m1 7979  ax-0id 7982

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-clel 2189

This theorem is referenced by:  ine0  8415  inelr  8605  muleqadd  8689  0p1e1  9098  iap0  9208  num0h  9462  nummul1c  9499  decrmac  9508  decmul1  9514  fz0tp  10191  fz0to4untppr  10193  fzo0to3tp  10289  rei  11046  imi  11047  resqrexlemover  11157  ef01bndlem  11902  efhalfpi  14975  sinq34lt0t  15007  ex-fac  15290