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Definition df-meet 14127
Description: Define poset meet. (Contributed by NM, 12-Sep-2011.)
Assertion
Ref Expression
df-meet  |-  meet  =  ( p  e.  _V  |->  ( x  e.  ( Base `  p ) ,  y  e.  ( Base `  p )  |->  ( ( glb `  p ) `
 { x ,  y } ) ) )
Distinct variable group:    x, p, y

Detailed syntax breakdown of Definition df-meet
StepHypRef Expression
1 cmee 14095 . 2  class  meet
2 vp . . 3  set  p
3 cvv 2801 . . 3  class  _V
4 vx . . . 4  set  x
5 vy . . . 4  set  y
62cv 1631 . . . . 5  class  p
7 cbs 13164 . . . . 5  class  Base
86, 7cfv 5271 . . . 4  class  ( Base `  p )
94cv 1631 . . . . . 6  class  x
105cv 1631 . . . . . 6  class  y
119, 10cpr 3654 . . . . 5  class  { x ,  y }
12 cglb 14093 . . . . . 6  class  glb
136, 12cfv 5271 . . . . 5  class  ( glb `  p )
1411, 13cfv 5271 . . . 4  class  ( ( glb `  p ) `
 { x ,  y } )
154, 5, 8, 8, 14cmpt2 5876 . . 3  class  ( x  e.  ( Base `  p
) ,  y  e.  ( Base `  p
)  |->  ( ( glb `  p ) `  {
x ,  y } ) )
162, 3, 15cmpt 4093 . 2  class  ( p  e.  _V  |->  ( x  e.  ( Base `  p
) ,  y  e.  ( Base `  p
)  |->  ( ( glb `  p ) `  {
x ,  y } ) ) )
171, 16wceq 1632 1  wff  meet  =  ( p  e.  _V  |->  ( x  e.  ( Base `  p ) ,  y  e.  ( Base `  p )  |->  ( ( glb `  p ) `
 { x ,  y } ) ) )
Colors of variables: wff set class
This definition is referenced by:  meetfval  14144
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