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Definition df-gcdOLD 24971
Description:  gcd OLD ( A ,  B
) is the largest natural number that evenly divides both  A and  B. (Contributed by Jeff Hoffman, 17-Jun-2008.)
Assertion
Ref Expression
df-gcdOLD  |-  gcd OLD ( A ,  B )  =  sup ( { x  e.  NN  | 
( ( A  /  x )  e.  NN  /\  ( B  /  x
)  e.  NN ) } ,  NN ,  <  )
Distinct variable groups:    x, A    x, B

Detailed syntax breakdown of Definition df-gcdOLD
StepHypRef Expression
1 cA . . 3  class  A
2 cB . . 3  class  B
31, 2cgcdOLD 24970 . 2  class  gcd OLD ( A ,  B )
4 vx . . . . . . . 8  set  x
54cv 1631 . . . . . . 7  class  x
6 cdiv 9439 . . . . . . 7  class  /
71, 5, 6co 5874 . . . . . 6  class  ( A  /  x )
8 cn 9762 . . . . . 6  class  NN
97, 8wcel 1696 . . . . 5  wff  ( A  /  x )  e.  NN
102, 5, 6co 5874 . . . . . 6  class  ( B  /  x )
1110, 8wcel 1696 . . . . 5  wff  ( B  /  x )  e.  NN
129, 11wa 358 . . . 4  wff  ( ( A  /  x )  e.  NN  /\  ( B  /  x )  e.  NN )
1312, 4, 8crab 2560 . . 3  class  { x  e.  NN  |  ( ( A  /  x )  e.  NN  /\  ( B  /  x )  e.  NN ) }
14 clt 8883 . . 3  class  <
1513, 8, 14csup 7209 . 2  class  sup ( { x  e.  NN  |  ( ( A  /  x )  e.  NN  /\  ( B  /  x )  e.  NN ) } ,  NN ,  <  )
163, 15wceq 1632 1  wff  gcd OLD ( A ,  B )  =  sup ( { x  e.  NN  | 
( ( A  /  x )  e.  NN  /\  ( B  /  x
)  e.  NN ) } ,  NN ,  <  )
Colors of variables: wff set class
This definition is referenced by:  ee7.2aOLD  24972
  Copyright terms: Public domain W3C validator