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Definition df-angle 25324
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 25323 . 2  class angle
2 vg . . 3  set  g
3 cibg 25273 . . 3  class Ibg
4 vw . . . 4  set  w
52cv 1618 . . . . . 6  class  g
6 cpoints 25222 . . . . . 6  class PPoints
75, 6cfv 4592 . . . . 5  class  (PPoints `  g
)
8 c3 9676 . . . . 5  class  3
9 cdwords 25150 . . . . 5  class dWords
107, 8, 9co 5710 . . . 4  class  ( (PPoints `  g )dWords 3 )
11 c2 9675 . . . . . . 7  class  2
124cv 1618 . . . . . . 7  class  w
1311, 12cfv 4592 . . . . . 6  class  ( w `
 2 )
14 c1 8618 . . . . . . 7  class  1
1514, 12cfv 4592 . . . . . 6  class  ( w `
 1 )
16 cray2 25317 . . . . . . 7  class ray
175, 16cfv 4592 . . . . . 6  class  (ray `  g )
1813, 15, 17co 5710 . . . . 5  class  ( ( w `  2 ) (ray `  g )
( w `  1
) )
198, 12cfv 4592 . . . . . 6  class  ( w `
 3 )
2013, 19, 17co 5710 . . . . 5  class  ( ( w `  2 ) (ray `  g )
( w `  3
) )
2118, 20cun 3076 . . . 4  class  ( ( ( w `  2
) (ray `  g
) ( w ` 
1 ) )  u.  ( ( w ` 
2 ) (ray `  g ) ( w `
 3 ) ) )
224, 10, 21cmpt 3974 . . 3  class  ( w  e.  ( (PPoints `  g
)dWords 3 )  |->  ( ( ( w ` 
2 ) (ray `  g ) ( w `
 1 ) )  u.  ( ( w `
 2 ) (ray
`  g ) ( w `  3 ) ) ) )
232, 3, 22cmpt 3974 . 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 1619 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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