Theorem addid2i 8120

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 8116	. 2 |- ( A e. CC -> ( 0 + A ) = A )
3	1, 2	ax-mp 5	1 |- ( 0 + A ) = A

Syntax hints:   = wceq 1364   e. wcel 2160  (class class class)co 5892   CCcc 7829   0cc0 7831   + caddc 7834

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 2171  ax-1cn 7924  ax-icn 7926  ax-addcl 7927  ax-mulcl 7929  ax-addcom 7931  ax-i2m1 7936  ax-0id 7939

This theorem depends on definitions:  df-bi 117  df-cleq 2182  df-clel 2185

This theorem is referenced by:  ine0  8371  inelr  8561  muleqadd  8645  0p1e1  9053  iap0  9162  num0h  9415  nummul1c  9452  decrmac  9461  decmul1  9467  fz0tp  10142  fz0to4untppr  10144  fzo0to3tp  10239  rei  10928  imi  10929  resqrexlemover  11039  ef01bndlem  11784  efhalfpi  14624  sinq34lt0t  14656  ex-fac  14884