Theorem addid1i 8098

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 8094	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1353   ∈ wcel 2148  (class class class)co 5874  ℂcc 7808  0cc0 7810   + caddc 7813

This theorem was proved from axioms:  ax-mp 5  ax-0id 7918

This theorem is referenced by:  1p0e1  9034  9p1e10  9385  num0u  9393  numnncl2  9405  decrmanc  9439  decaddi  9442  decaddci  9443  decmul1  9446  decmulnc  9449  fsumrelem  11478  demoivreALT  11780  sinhalfpilem  14182  efipi  14192