Theorem addid1i 7928

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 e. CC

Assertion

Ref	Expression
addid1i	|- ( A + 0 ) = A

Proof of Theorem addid1i

Step	Hyp	Ref	Expression
1		mul.1	. 2 |- A e. CC
2		addid1 7924	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1332   e. wcel 1481  (class class class)co 5782   CCcc 7642   0cc0 7644   + caddc 7647

This theorem was proved from axioms:  ax-mp 5  ax-0id 7752

This theorem is referenced by:  1p0e1  8860  9p1e10  9208  num0u  9216  numnncl2  9228  decrmanc  9262  decaddi  9265  decaddci  9266  decmul1  9269  decmulnc  9272  fsumrelem  11272  demoivreALT  11516  sinhalfpilem  12920  efipi  12930