Theorem addlidi 8365

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
addlidi	|- ( 0 + A ) = A

Proof of Theorem addlidi

Step	Hyp	Ref	Expression
1		mul.1	. 2 |- A e. CC
2		addlid 8361	. 2 |- ( A e. CC -> ( 0 + A ) = A )
3	1, 2	ax-mp 5	1 |- ( 0 + A ) = A

Syntax hints:   = wceq 1398   e. wcel 2202  (class class class)co 6028   CCcc 8073   0cc0 8075   + caddc 8078

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2213  ax-1cn 8168  ax-icn 8170  ax-addcl 8171  ax-mulcl 8173  ax-addcom 8175  ax-i2m1 8180  ax-0id 8183

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-clel 2227

This theorem is referenced by:  ine0  8616  inelr  8807  muleqadd  8891  0p1e1  9300  iap0  9410  num0h  9665  nummul1c  9702  decrmac  9711  decmul1  9717  fz0tp  10400  fz0to4untppr  10402  fzo0to3tp  10508  cats1fvn  11392  rei  11520  imi  11521  resqrexlemover  11631  ef01bndlem  12378  5ndvds3  12556  dec5dvds2  13047  2exp11  13070  2exp16  13071  efhalfpi  15590  sinq34lt0t  15622  ex-fac  16422