Theorem addridi 8166

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 8162	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1364   ∈ wcel 2167  (class class class)co 5922  ℂcc 7875  0cc0 7877   + caddc 7880

This theorem was proved from axioms:  ax-mp 5  ax-0id 7985

This theorem is referenced by:  1p0e1  9103  9p1e10  9456  num0u  9464  numnncl2  9476  decrmanc  9510  decaddi  9513  decaddci  9514  decmul1  9517  decmulnc  9520  fsumrelem  11620  demoivreALT  11923  decsplit0  12572  sinhalfpilem  15002  efipi  15012