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Theorem addid2i 7217
Description: 0 is a left identity for addition. (Contributed by NM, 3-Jan-2013.)
Hypothesis
Ref Expression
mul.1 𝐴 ∈ ℂ
Assertion
Ref Expression
addid2i (0 + 𝐴) = 𝐴

Proof of Theorem addid2i
StepHypRef Expression
1 mul.1 . 2 𝐴 ∈ ℂ
2 addid2 7213 . 2 (𝐴 ∈ ℂ → (0 + 𝐴) = 𝐴)
31, 2ax-mp 7 1 (0 + 𝐴) = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1259  wcel 1409  (class class class)co 5540  cc 6945  0cc0 6947   + caddc 6950
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-ext 2038  ax-1cn 7035  ax-icn 7037  ax-addcl 7038  ax-mulcl 7040  ax-addcom 7042  ax-i2m1 7047  ax-0id 7050
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-clel 2052
This theorem is referenced by:  ine0  7463  inelr  7649  muleqadd  7723  0p1e1  8104  iap0  8205  num0h  8438  nummul1c  8475  decrmac  8484  decmul1  8490  fz0tp  9083  fzo0to3tp  9177  rei  9727  imi  9728  resqrexlemover  9837  ex-fac  10281
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