Theorem addid1i 8000

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

Step	Hyp	Ref	Expression
1		mul.1	. 2 ⊢ 𝐴 ∈ ℂ
2		addid1 7996	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1335   ∈ wcel 2128  (class class class)co 5818  ℂcc 7713  0cc0 7715   + caddc 7718

This theorem was proved from axioms:  ax-mp 5  ax-0id 7823

This theorem is referenced by:  1p0e1  8932  9p1e10  9280  num0u  9288  numnncl2  9300  decrmanc  9334  decaddi  9337  decaddci  9338  decmul1  9341  decmulnc  9344  fsumrelem  11350  demoivreALT  11652  sinhalfpilem  13072  efipi  13082