Theorem addid2i 8037

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		addid2 8033	. 2 |- ( A e. CC -> ( 0 + A ) = A )
3	1, 2	ax-mp 5	1 |- ( 0 + A ) = A

Syntax hints:   = wceq 1343   e. wcel 2136  (class class class)co 5841   CCcc 7747   0cc0 7749   + caddc 7752

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-17 1514  ax-ial 1522  ax-ext 2147  ax-1cn 7842  ax-icn 7844  ax-addcl 7845  ax-mulcl 7847  ax-addcom 7849  ax-i2m1 7854  ax-0id 7857

This theorem depends on definitions:  df-bi 116  df-cleq 2158  df-clel 2161

This theorem is referenced by:  ine0  8288  inelr  8478  muleqadd  8561  0p1e1  8967  iap0  9076  num0h  9329  nummul1c  9366  decrmac  9375  decmul1  9381  fz0tp  10053  fz0to4untppr  10055  fzo0to3tp  10150  rei  10837  imi  10838  resqrexlemover  10948  ef01bndlem  11693  efhalfpi  13320  sinq34lt0t  13352  ex-fac  13569