Theorem addridi 8314

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
addridi	|- ( A + 0 ) = A

Proof of Theorem addridi

Step	Hyp	Ref	Expression
1		mul.1	. 2 |- A e. CC
2		addrid 8310	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1395   e. wcel 2200  (class class class)co 6013   CCcc 8023   0cc0 8025   + caddc 8028

This theorem was proved from axioms:  ax-mp 5  ax-0id 8133

This theorem is referenced by:  1p0e1  9252  9p1e10  9606  num0u  9614  numnncl2  9626  decrmanc  9660  decaddi  9663  decaddci  9664  decmul1  9667  decmulnc  9670  fsumrelem  12025  demoivreALT  12328  decsplit0  12993  sinhalfpilem  15508  efipi  15518