ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  addid1i Unicode version

Theorem addid1i 8061
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
StepHypRef Expression
1 mul.1 . 2  |-  A  e.  CC
2 addid1 8057 . 2  |-  ( A  e.  CC  ->  ( A  +  0 )  =  A )
31, 2ax-mp 5 1  |-  ( A  +  0 )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1348    e. wcel 2141  (class class class)co 5853   CCcc 7772   0cc0 7774    + caddc 7777
This theorem was proved from axioms:  ax-mp 5  ax-0id 7882
This theorem is referenced by:  1p0e1  8994  9p1e10  9345  num0u  9353  numnncl2  9365  decrmanc  9399  decaddi  9402  decaddci  9403  decmul1  9406  decmulnc  9409  fsumrelem  11434  demoivreALT  11736  sinhalfpilem  13506  efipi  13516
  Copyright terms: Public domain W3C validator