Theorem addid1i 8163

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		addrid 8159	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1364   e. wcel 2164  (class class class)co 5919   CCcc 7872   0cc0 7874   + caddc 7877

This theorem was proved from axioms:  ax-mp 5  ax-0id 7982

This theorem is referenced by:  1p0e1  9100  9p1e10  9453  num0u  9461  numnncl2  9473  decrmanc  9507  decaddi  9510  decaddci  9511  decmul1  9514  decmulnc  9517  fsumrelem  11617  demoivreALT  11920  sinhalfpilem  14967  efipi  14977