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Definition df-join 14110
Description: Define poset join. (Contributed by NM, 12-Sep-2011.)
Assertion
Ref Expression
df-join  |-  join  =  ( p  e.  _V  |->  ( x  e.  ( Base `  p ) ,  y  e.  ( Base `  p )  |->  ( ( lub `  p ) `
 { x ,  y } ) ) )
Distinct variable group:    x, p, y

Detailed syntax breakdown of Definition df-join
StepHypRef Expression
1 cjn 14078 . 2  class  join
2 vp . . 3  set  p
3 cvv 2788 . . 3  class  _V
4 vx . . . 4  set  x
5 vy . . . 4  set  y
62cv 1622 . . . . 5  class  p
7 cbs 13148 . . . . 5  class  Base
86, 7cfv 5255 . . . 4  class  ( Base `  p )
94cv 1622 . . . . . 6  class  x
105cv 1622 . . . . . 6  class  y
119, 10cpr 3641 . . . . 5  class  { x ,  y }
12 club 14076 . . . . . 6  class  lub
136, 12cfv 5255 . . . . 5  class  ( lub `  p )
1411, 13cfv 5255 . . . 4  class  ( ( lub `  p ) `
 { x ,  y } )
154, 5, 8, 8, 14cmpt2 5860 . . 3  class  ( x  e.  ( Base `  p
) ,  y  e.  ( Base `  p
)  |->  ( ( lub `  p ) `  {
x ,  y } ) )
162, 3, 15cmpt 4077 . 2  class  ( p  e.  _V  |->  ( x  e.  ( Base `  p
) ,  y  e.  ( Base `  p
)  |->  ( ( lub `  p ) `  {
x ,  y } ) ) )
171, 16wceq 1623 1  wff  join  =  ( p  e.  _V  |->  ( x  e.  ( Base `  p ) ,  y  e.  ( Base `  p )  |->  ( ( lub `  p ) `
 { x ,  y } ) ) )
Colors of variables: wff set class
This definition is referenced by:  joinfval  14121
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