Theorem addid2i 8094

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 8090	. 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 5870   CCcc 7804   0cc0 7806   + caddc 7809

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 7899  ax-icn 7901  ax-addcl 7902  ax-mulcl 7904  ax-addcom 7906  ax-i2m1 7911  ax-0id 7914

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

This theorem is referenced by:  ine0  8345  inelr  8535  muleqadd  8619  0p1e1  9027  iap0  9136  num0h  9389  nummul1c  9426  decrmac  9435  decmul1  9441  fz0tp  10115  fz0to4untppr  10117  fzo0to3tp  10212  rei  10899  imi  10900  resqrexlemover  11010  ef01bndlem  11755  efhalfpi  14002  sinq34lt0t  14034  ex-fac  14251