Theorem addridi 8304

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 8300	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1395   ∈ wcel 2200  (class class class)co 6010  ℂcc 8013  0cc0 8015   + caddc 8018

This theorem was proved from axioms:  ax-mp 5  ax-0id 8123

This theorem is referenced by:  1p0e1  9242  9p1e10  9596  num0u  9604  numnncl2  9616  decrmanc  9650  decaddi  9653  decaddci  9654  decmul1  9657  decmulnc  9660  fsumrelem  12003  demoivreALT  12306  decsplit0  12971  sinhalfpilem  15486  efipi  15496