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Definition df-omul 6140
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 6133 . 2  class  .o
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 con0 4164 . . 3  class  On
53cv 1286 . . . 4  class  y
6 vz . . . . . 6  setvar  z
7 cvv 2615 . . . . . 6  class  _V
86cv 1286 . . . . . . 7  class  z
92cv 1286 . . . . . . 7  class  x
10 coa 6132 . . . . . . 7  class  +o
118, 9, 10co 5613 . . . . . 6  class  ( z  +o  x )
126, 7, 11cmpt 3874 . . . . 5  class  ( z  e.  _V  |->  ( z  +o  x ) )
13 c0 3275 . . . . 5  class  (/)
1412, 13crdg 6088 . . . 4  class  rec (
( z  e.  _V  |->  ( z  +o  x
) ) ,  (/) )
155, 14cfv 4981 . . 3  class  ( rec ( ( z  e. 
_V  |->  ( z  +o  x ) ) ,  (/) ) `  y )
162, 3, 4, 4, 15cmpt2 5615 . 2  class  ( x  e.  On ,  y  e.  On  |->  ( rec ( ( z  e. 
_V  |->  ( z  +o  x ) ) ,  (/) ) `  y ) )
171, 16wceq 1287 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  6165  omexg  6166  omv  6170
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