Theorem addid1i 8161

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		addrid 8157	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1364   ∈ wcel 2164  (class class class)co 5918  ℂcc 7870  0cc0 7872   + caddc 7875

This theorem was proved from axioms:  ax-mp 5  ax-0id 7980

This theorem is referenced by:  1p0e1  9098  9p1e10  9450  num0u  9458  numnncl2  9470  decrmanc  9504  decaddi  9507  decaddci  9508  decmul1  9511  decmulnc  9514  fsumrelem  11614  demoivreALT  11917  sinhalfpilem  14926  efipi  14936