Theorem addridi 8321

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
addridi	⊢ (𝐴 + 0) = 𝐴

Proof of Theorem addridi

Step	Hyp	Ref	Expression
1		mul.1	. 2 ⊢ 𝐴 ∈ ℂ
2		addrid 8317	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1397   ∈ wcel 2202  (class class class)co 6018  ℂcc 8030  0cc0 8032   + caddc 8035

This theorem was proved from axioms:  ax-mp 5  ax-0id 8140

This theorem is referenced by:  1p0e1  9259  9p1e10  9613  num0u  9621  numnncl2  9633  decrmanc  9667  decaddi  9670  decaddci  9671  decmul1  9674  decmulnc  9677  fsumrelem  12034  demoivreALT  12337  decsplit0  13002  sinhalfpilem  15518  efipi  15528