Theorem addid1i 8017

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 8013	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1335   e. wcel 2128  (class class class)co 5824   CCcc 7730   0cc0 7732   + caddc 7735

This theorem was proved from axioms:  ax-mp 5  ax-0id 7840

This theorem is referenced by:  1p0e1  8949  9p1e10  9297  num0u  9305  numnncl2  9317  decrmanc  9351  decaddi  9354  decaddci  9355  decmul1  9358  decmulnc  9361  fsumrelem  11368  demoivreALT  11670  sinhalfpilem  13123  efipi  13133