Theorem addid1i 7907

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 7903	. 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 5774  ℂcc 7621  0cc0 7623   + caddc 7626

This theorem was proved from axioms:  ax-mp 5  ax-0id 7731

This theorem is referenced by:  1p0e1  8839  9p1e10  9187  num0u  9195  numnncl2  9207  decrmanc  9241  decaddi  9244  decaddci  9245  decmul1  9248  decmulnc  9251  fsumrelem  11243  demoivreALT  11483  sinhalfpilem  12875  efipi  12885