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Definition df-angle 25569
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 25568 . 2  class angle
2 vg . . 3  set  g
3 cibg 25518 . . 3  class Ibg
4 vw . . . 4  set  w
52cv 1622 . . . . . 6  class  g
6 cpoints 25467 . . . . . 6  class PPoints
75, 6cfv 5221 . . . . 5  class  (PPoints `  g
)
8 c3 9792 . . . . 5  class  3
9 cdwords 25395 . . . . 5  class dWords
107, 8, 9co 5820 . . . 4  class  ( (PPoints `  g )dWords 3 )
11 c2 9791 . . . . . . 7  class  2
124cv 1622 . . . . . . 7  class  w
1311, 12cfv 5221 . . . . . 6  class  ( w `
 2 )
14 c1 8734 . . . . . . 7  class  1
1514, 12cfv 5221 . . . . . 6  class  ( w `
 1 )
16 cray2 25562 . . . . . . 7  class ray
175, 16cfv 5221 . . . . . 6  class  (ray `  g )
1813, 15, 17co 5820 . . . . 5  class  ( ( w `  2 ) (ray `  g )
( w `  1
) )
198, 12cfv 5221 . . . . . 6  class  ( w `
 3 )
2013, 19, 17co 5820 . . . . 5  class  ( ( w `  2 ) (ray `  g )
( w `  3
) )
2118, 20cun 3151 . . . 4  class  ( ( ( w `  2
) (ray `  g
) ( w ` 
1 ) )  u.  ( ( w ` 
2 ) (ray `  g ) ( w `
 3 ) ) )
224, 10, 21cmpt 4078 . . 3  class  ( w  e.  ( (PPoints `  g
)dWords 3 )  |->  ( ( ( w ` 
2 ) (ray `  g ) ( w `
 1 ) )  u.  ( ( w `
 2 ) (ray
`  g ) ( w `  3 ) ) ) )
232, 3, 22cmpt 4078 . 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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