Theorem addlidi 8277

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 8273	. 2 |- ( A e. CC -> ( 0 + A ) = A )
3	1, 2	ax-mp 5	1 |- ( 0 + A ) = A

Syntax hints:   = wceq 1395   e. wcel 2200  (class class class)co 5994   CCcc 7985   0cc0 7987   + caddc 7990

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580  ax-ext 2211  ax-1cn 8080  ax-icn 8082  ax-addcl 8083  ax-mulcl 8085  ax-addcom 8087  ax-i2m1 8092  ax-0id 8095

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-clel 2225

This theorem is referenced by:  ine0  8528  inelr  8719  muleqadd  8803  0p1e1  9212  iap0  9322  num0h  9577  nummul1c  9614  decrmac  9623  decmul1  9629  fz0tp  10306  fz0to4untppr  10308  fzo0to3tp  10412  cats1fvn  11282  rei  11396  imi  11397  resqrexlemover  11507  ef01bndlem  12253  5ndvds3  12431  dec5dvds2  12922  2exp11  12945  2exp16  12946  efhalfpi  15458  sinq34lt0t  15490  ex-fac  16022