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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
StepHypRef Expression
1 mul.1 . 2  |-  A  e.  CC
2 addid2 7303 . 2  |-  ( A  e.  CC  ->  (
0  +  A )  =  A )
31, 2ax-mp 7 1  |-  ( 0  +  A )  =  A
Colors of variables: wff set class
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
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