Theorem addid1i 7897

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 7893	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1331   ∈ wcel 1480  (class class class)co 5767  ℂcc 7611  0cc0 7613   + caddc 7616

This theorem was proved from axioms:  ax-mp 5  ax-0id 7721

This theorem is referenced by:  1p0e1  8829  9p1e10  9177  num0u  9185  numnncl2  9197  decrmanc  9231  decaddi  9234  decaddci  9235  decmul1  9238  decmulnc  9241  fsumrelem  11233  demoivreALT  11469  sinhalfpilem  12861  efipi  12871