Theorem addid2i 7307

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		addid2 7303	. 2 |- ( A e. CC -> ( 0 + A ) = A )
3	1, 2	ax-mp 7	1 |- ( 0 + A ) = A

Syntax hints:   = wceq 1285   e. wcel 1434  (class class class)co 5537   CCcc 7030   0cc0 7032   + caddc 7035

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064  ax-1cn 7120  ax-icn 7122  ax-addcl 7123  ax-mulcl 7125  ax-addcom 7127  ax-i2m1 7132  ax-0id 7135

This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-clel 2078

This theorem is referenced by:  ine0  7554  inelr  7740  muleqadd  7814  0p1e1  8209  iap0  8310  num0h  8558  nummul1c  8595  decrmac  8604  decmul1  8610  fz0tp  9201  fzo0to3tp  9294  rei  9913  imi  9914  resqrexlemover  10023  ex-fac  10701