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Theorem addid2 7303
Description:  0 is a left identity for addition. (Contributed by Scott Fenton, 3-Jan-2013.)
Assertion
Ref Expression
addid2  |-  ( A  e.  CC  ->  (
0  +  A )  =  A )

Proof of Theorem addid2
StepHypRef Expression
1 0cn 7162 . . 3  |-  0  e.  CC
2 addcom 7301 . . 3  |-  ( ( A  e.  CC  /\  0  e.  CC )  ->  ( A  +  0 )  =  ( 0  +  A ) )
31, 2mpan2 416 . 2  |-  ( A  e.  CC  ->  ( A  +  0 )  =  ( 0  +  A ) )
4 addid1 7302 . 2  |-  ( A  e.  CC  ->  ( A  +  0 )  =  A )
53, 4eqtr3d 2116 1  |-  ( A  e.  CC  ->  (
0  +  A )  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = 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:  readdcan  7304  addid2i  7307  addid2d  7314  cnegexlem1  7339  cnegexlem2  7340  addcan  7344  negneg  7414  fzoaddel2  9268  divfl0  9367  modqid  9420  isumrblem  10326  gcdid  10510
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