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Definition df-omul 6480
Description: Define the ordinal multiplication operation. (Contributed by NM, 26-Aug-1995.)
Assertion
Ref Expression
df-omul  |-  .o  =  ( x  e.  On ,  y  e.  On  |->  ( rec ( ( z  e.  _V  |->  ( z  +o  x ) ) ,  (/) ) `  y
) )
Distinct variable group:    x, y, z

Detailed syntax breakdown of Definition df-omul
StepHypRef Expression
1 comu 6473 . 2  class  .o
2 vx . . 3  set  x
3 vy . . 3  set  y
4 con0 4391 . . 3  class  On
53cv 1622 . . . 4  class  y
6 vz . . . . . 6  set  z
7 cvv 2789 . . . . . 6  class  _V
86cv 1622 . . . . . . 7  class  z
92cv 1622 . . . . . . 7  class  x
10 coa 6472 . . . . . . 7  class  +o
118, 9, 10co 5820 . . . . . 6  class  ( z  +o  x )
126, 7, 11cmpt 4078 . . . . 5  class  ( z  e.  _V  |->  ( z  +o  x ) )
13 c0 3456 . . . . 5  class  (/)
1412, 13crdg 6418 . . . 4  class  rec (
( z  e.  _V  |->  ( z  +o  x
) ) ,  (/) )
155, 14cfv 5221 . . 3  class  ( rec ( ( z  e. 
_V  |->  ( z  +o  x ) ) ,  (/) ) `  y )
162, 3, 4, 4, 15cmpt2 5822 . 2  class  ( x  e.  On ,  y  e.  On  |->  ( rec ( ( z  e. 
_V  |->  ( z  +o  x ) ) ,  (/) ) `  y ) )
171, 16wceq 1623 1  wff  .o  =  ( x  e.  On ,  y  e.  On  |->  ( rec ( ( z  e.  _V  |->  ( z  +o  x ) ) ,  (/) ) `  y
) )
Colors of variables: wff set class
This definition is referenced by:  fnom  6504  omv  6507
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