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Theorem addid2i 6953
Description: 0 is a left identity for addition. (Contributed by NM, 3-Jan-2013.)
Hypothesis
Ref Expression
mul.1 A
Assertion
Ref Expression
addid2i (0 + A) = A

Proof of Theorem addid2i
StepHypRef Expression
1 mul.1 . 2 A
2 addid2 6949 . 2 (A ℂ → (0 + A) = A)
31, 2ax-mp 7 1 (0 + A) = A
Colors of variables: wff set class
Syntax hints:   = 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:  ine0  7187  inelr  7368  muleqadd  7431  0p1e1  7809  iap0  7925  num0h  8153  nummul1c  8179  fz0tp  8751  fzo0to3tp  8845  rei  9127  imi  9128
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