Theorem addridi 8432

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 8428	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1398   ∈ wcel 2205  (class class class)co 6058  ℂcc 8141  0cc0 8143   + caddc 8146

This theorem was proved from axioms:  ax-mp 5  ax-0id 8251

This theorem is referenced by:  1p0e1  9373  9p1e10  9732  num0u  9740  numnncl2  9752  decrmanc  9786  decaddi  9789  decaddci  9790  decmul1  9793  decmulnc  9796  fsumrelem  12185  demoivreALT  12488  decsplit0  13153  ballotfilemth  13228  sinhalfpilem  15785  efipi  15795