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Definition df-oadd 6480
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 6473 . 2  class  +o
2 vx . . 3  set  x
3 vy . . 3  set  y
4 con0 4393 . . 3  class  On
53cv 1624 . . . 4  class  y
6 vz . . . . . 6  set  z
7 cvv 2791 . . . . . 6  class  _V
86cv 1624 . . . . . . 7  class  z
98csuc 4395 . . . . . 6  class  suc  z
106, 7, 9cmpt 4080 . . . . 5  class  ( z  e.  _V  |->  suc  z
)
112cv 1624 . . . . 5  class  x
1210, 11crdg 6419 . . . 4  class  rec (
( z  e.  _V  |->  suc  z ) ,  x
)
135, 12cfv 5223 . . 3  class  ( rec ( ( z  e. 
_V  |->  suc  z ) ,  x ) `  y
)
142, 3, 4, 4, 13cmpt2 5823 . 2  class  ( x  e.  On ,  y  e.  On  |->  ( rec ( ( z  e. 
_V  |->  suc  z ) ,  x ) `  y
) )
151, 14wceq 1625 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  6504  oav  6507
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