Theorem addridi 8431

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 8427	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1398   e. wcel 2205  (class class class)co 6058   CCcc 8141   0cc0 8143   + caddc 8146

This theorem was proved from axioms:  ax-mp 5  ax-0id 8251

This theorem is referenced by:  1p0e1  9370  9p1e10  9729  num0u  9737  numnncl2  9749  decrmanc  9783  decaddi  9786  decaddci  9787  decmul1  9790  decmulnc  9793  fsumrelem  12182  demoivreALT  12485  decsplit0  13150  ballotfilemth  13225  sinhalfpilem  15768  efipi  15778