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Theorem addid2i 7156
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 7152 . 2  |-  ( A  e.  CC  ->  (
0  +  A )  =  A )
31, 2ax-mp 7 1  |-  ( 0  +  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1243    e. wcel 1393  (class class class)co 5512   CCcc 6887   0cc0 6889    + caddc 6892
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-1cn 6977  ax-icn 6979  ax-addcl 6980  ax-mulcl 6982  ax-addcom 6984  ax-i2m1 6989  ax-0id 6992
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036
This theorem is referenced by:  ine0  7391  inelr  7575  muleqadd  7649  0p1e1  8031  iap0  8148  num0h  8377  nummul1c  8403  fz0tp  8981  fzo0to3tp  9075  rei  9499  imi  9500  resqrexlemover  9608
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