Theorem addridi 8256

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 8252	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1375   ∈ wcel 2180  (class class class)co 5974  ℂcc 7965  0cc0 7967   + caddc 7970

This theorem was proved from axioms:  ax-mp 5  ax-0id 8075

This theorem is referenced by:  1p0e1  9194  9p1e10  9548  num0u  9556  numnncl2  9568  decrmanc  9602  decaddi  9605  decaddci  9606  decmul1  9609  decmulnc  9612  fsumrelem  11948  demoivreALT  12251  decsplit0  12916  sinhalfpilem  15430  efipi  15440