Theorem addid2i 6953

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

Step	Hyp	Ref	Expression
1		mul.1	. 2 ⊢ A ∈ ℂ
2		addid2 6949	. 2 ⊢ (A ∈ ℂ → (0 + A) = A)
3	1, 2	ax-mp 7	1 ⊢ (0 + A) = A

Syntax hints:   = wceq 1242   ∈ wcel 1390  (class class class)co 5455  ℂcc 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