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Theorem addid1i 7216
Description: 0 is an additive identity. (Contributed by NM, 23-Nov-1994.) (Revised by Scott Fenton, 3-Jan-2013.)
Hypothesis
Ref Expression
mul.1 𝐴 ∈ ℂ
Assertion
Ref Expression
addid1i (𝐴 + 0) = 𝐴

Proof of Theorem addid1i
StepHypRef Expression
1 mul.1 . 2 𝐴 ∈ ℂ
2 addid1 7212 . 2 (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
31, 2ax-mp 7 1 (𝐴 + 0) = 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-mp 7  ax-0id 7050
This theorem is referenced by:  1p0e1  8105  9p1e10  8429  num0u  8437  numnncl2  8449  decrmanc  8483  decaddi  8486  decaddci  8487  decmul1  8490  decmulnc  8493
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