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

Definition df-omul 5945
Description: Define the ordinal multiplication operation. (Contributed by NM, 26-Aug-1995.)
Assertion
Ref Expression
df-omul  .o  On ,  On  |->  rec  _V  |->  +o  ,  (/) `
Distinct variable group:   ,,

Detailed syntax breakdown of Definition df-omul
StepHypRef Expression
1 comu 5938 . 2  .o
2 vx . . 3  setvar
3 vy . . 3  setvar
4 con0 4066 . . 3  On
53cv 1241 . . . 4
6 vz . . . . . 6  setvar
7 cvv 2551 . . . . . 6  _V
86cv 1241 . . . . . . 7
92cv 1241 . . . . . . 7
10 coa 5937 . . . . . . 7  +o
118, 9, 10co 5455 . . . . . 6  +o
126, 7, 11cmpt 3809 . . . . 5  _V  |->  +o
13 c0 3218 . . . . 5  (/)
1412, 13crdg 5896 . . . 4  rec  _V  |->  +o  ,  (/)
155, 14cfv 4845 . . 3  rec 
_V  |->  +o  ,  (/) `
162, 3, 4, 4, 15cmpt2 5457 . 2  On ,  On  |->  rec 
_V  |->  +o  ,  (/) `
171, 16wceq 1242 1  .o  On ,  On  |->  rec  _V  |->  +o  ,  (/) `
Colors of variables: wff set class
This definition is referenced by:  fnom  5969  omexg  5970  omv  5974
  Copyright terms: Public domain W3C validator