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

Definition df-oadd 6141
Description: Define the ordinal addition operation. (Contributed by NM, 3-May-1995.)
Assertion
Ref Expression
df-oadd  |-  +o  =  ( x  e.  On ,  y  e.  On  |->  ( rec ( ( z  e.  _V  |->  suc  z
) ,  x ) `
 y ) )
Distinct variable group:    x, y, z

Detailed syntax breakdown of Definition df-oadd
StepHypRef Expression
1 coa 6134 . 2  class  +o
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 con0 4166 . . 3  class  On
53cv 1286 . . . 4  class  y
6 vz . . . . . 6  setvar  z
7 cvv 2615 . . . . . 6  class  _V
86cv 1286 . . . . . . 7  class  z
98csuc 4168 . . . . . 6  class  suc  z
106, 7, 9cmpt 3876 . . . . 5  class  ( z  e.  _V  |->  suc  z
)
112cv 1286 . . . . 5  class  x
1210, 11crdg 6090 . . . 4  class  rec (
( z  e.  _V  |->  suc  z ) ,  x
)
135, 12cfv 4983 . . 3  class  ( rec ( ( z  e. 
_V  |->  suc  z ) ,  x ) `  y
)
142, 3, 4, 4, 13cmpt2 5617 . 2  class  ( x  e.  On ,  y  e.  On  |->  ( rec ( ( z  e. 
_V  |->  suc  z ) ,  x ) `  y
) )
151, 14wceq 1287 1  wff  +o  =  ( x  e.  On ,  y  e.  On  |->  ( rec ( ( z  e.  _V  |->  suc  z
) ,  x ) `
 y ) )
Colors of variables: wff set class
This definition is referenced by:  fnoa  6164  oaexg  6165  oav  6171
  Copyright terms: Public domain W3C validator