Theorem addridi 8364

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 8360	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1398   e. wcel 2202  (class class class)co 6028   CCcc 8073   0cc0 8075   + caddc 8078

This theorem was proved from axioms:  ax-mp 5  ax-0id 8183

This theorem is referenced by:  1p0e1  9302  9p1e10  9656  num0u  9664  numnncl2  9676  decrmanc  9710  decaddi  9713  decaddci  9714  decmul1  9717  decmulnc  9720  fsumrelem  12093  demoivreALT  12396  decsplit0  13061  sinhalfpilem  15582  efipi  15592