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Theorem addid2 6949
Description: 0 is a left identity for addition. (Contributed by Scott Fenton, 3-Jan-2013.)
Assertion
Ref Expression
addid2 (A ℂ → (0 + A) = A)

Proof of Theorem addid2
StepHypRef Expression
1 0cn 6817 . . 3 0
2 addcom 6947 . . 3 ((A 0 ℂ) → (A + 0) = (0 + A))
31, 2mpan2 401 . 2 (A ℂ → (A + 0) = (0 + A))
4 addid1 6948 . 2 (A ℂ → (A + 0) = A)
53, 4eqtr3d 2071 1 (A ℂ → (0 + A) = A)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   wcel 1390  (class class class)co 5455  cc 6709  0cc0 6711   + caddc 6714
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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019  ax-1cn 6776  ax-icn 6778  ax-addcl 6779  ax-mulcl 6781  ax-addcom 6783  ax-i2m1 6788  ax-0id 6791
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033
This theorem is referenced by:  readdcan  6950  addid2i  6953  addid2d  6960  cnegexlem1  6983  cnegexlem2  6984  addcan  6988  negneg  7057  fzoaddel2  8819
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