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Definition df-angle 26158
Description: Definition of an angle. Definition 17 of [AitkenIBG] p. 10. The angles can't be degenerated. Contrary to the concept of degenerated line or segment, the concept of degenerated angle no longer simplifies the wording. (For my private use only. Don't use.) (Contributed by FL, 7-Apr-2016.)
Assertion
Ref Expression
df-angle  |- angle  =  ( g  e. Ibg  |->  ( w  e.  ( (PPoints `  g
)dWords 3 )  |->  ( ( ( w ` 
2 ) (ray `  g ) ( w `
 1 ) )  u.  ( ( w `
 2 ) (ray
`  g ) ( w `  3 ) ) ) ) )
Distinct variable group:    w, g

Detailed syntax breakdown of Definition df-angle
StepHypRef Expression
1 cangle 26157 . 2  class angle
2 vg . . 3  set  g
3 cibg 26107 . . 3  class Ibg
4 vw . . . 4  set  w
52cv 1622 . . . . . 6  class  g
6 cpoints 26056 . . . . . 6  class PPoints
75, 6cfv 5255 . . . . 5  class  (PPoints `  g
)
8 c3 9796 . . . . 5  class  3
9 cdwords 25984 . . . . 5  class dWords
107, 8, 9co 5858 . . . 4  class  ( (PPoints `  g )dWords 3 )
11 c2 9795 . . . . . . 7  class  2
124cv 1622 . . . . . . 7  class  w
1311, 12cfv 5255 . . . . . 6  class  ( w `
 2 )
14 c1 8738 . . . . . . 7  class  1
1514, 12cfv 5255 . . . . . 6  class  ( w `
 1 )
16 cray2 26151 . . . . . . 7  class ray
175, 16cfv 5255 . . . . . 6  class  (ray `  g )
1813, 15, 17co 5858 . . . . 5  class  ( ( w `  2 ) (ray `  g )
( w `  1
) )
198, 12cfv 5255 . . . . . 6  class  ( w `
 3 )
2013, 19, 17co 5858 . . . . 5  class  ( ( w `  2 ) (ray `  g )
( w `  3
) )
2118, 20cun 3150 . . . 4  class  ( ( ( w `  2
) (ray `  g
) ( w ` 
1 ) )  u.  ( ( w ` 
2 ) (ray `  g ) ( w `
 3 ) ) )
224, 10, 21cmpt 4077 . . 3  class  ( w  e.  ( (PPoints `  g
)dWords 3 )  |->  ( ( ( w ` 
2 ) (ray `  g ) ( w `
 1 ) )  u.  ( ( w `
 2 ) (ray
`  g ) ( w `  3 ) ) ) )
232, 3, 22cmpt 4077 . 2  class  ( g  e. Ibg  |->  ( w  e.  ( (PPoints `  g
)dWords 3 )  |->  ( ( ( w ` 
2 ) (ray `  g ) ( w `
 1 ) )  u.  ( ( w `
 2 ) (ray
`  g ) ( w `  3 ) ) ) ) )
241, 23wceq 1623 1  wff angle  =  ( g  e. Ibg  |->  ( w  e.  ( (PPoints `  g
)dWords 3 )  |->  ( ( ( w ` 
2 ) (ray `  g ) ( w `
 1 ) )  u.  ( ( w `
 2 ) (ray
`  g ) ( w `  3 ) ) ) ) )
Colors of variables: wff set class
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