Theorem addid2i 8102

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 8098	. 2 |- ( A e. CC -> ( 0 + A ) = A )
3	1, 2	ax-mp 5	1 |- ( 0 + A ) = A

Syntax hints:   = wceq 1353   e. wcel 2148  (class class class)co 5877   CCcc 7811   0cc0 7813   + caddc 7816

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-1cn 7906  ax-icn 7908  ax-addcl 7909  ax-mulcl 7911  ax-addcom 7913  ax-i2m1 7918  ax-0id 7921

This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-clel 2173

This theorem is referenced by:  ine0  8353  inelr  8543  muleqadd  8627  0p1e1  9035  iap0  9144  num0h  9397  nummul1c  9434  decrmac  9443  decmul1  9449  fz0tp  10124  fz0to4untppr  10126  fzo0to3tp  10221  rei  10910  imi  10911  resqrexlemover  11021  ef01bndlem  11766  efhalfpi  14259  sinq34lt0t  14291  ex-fac  14519