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Definition df-angle 25526
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 25525 . 2  class angle
2 vg . . 3  set  g
3 cibg 25475 . . 3  class Ibg
4 vw . . . 4  set  w
52cv 1618 . . . . . 6  class  g
6 cpoints 25424 . . . . . 6  class PPoints
75, 6cfv 4673 . . . . 5  class  (PPoints `  g
)
8 c3 9764 . . . . 5  class  3
9 cdwords 25352 . . . . 5  class dWords
107, 8, 9co 5792 . . . 4  class  ( (PPoints `  g )dWords 3 )
11 c2 9763 . . . . . . 7  class  2
124cv 1618 . . . . . . 7  class  w
1311, 12cfv 4673 . . . . . 6  class  ( w `
 2 )
14 c1 8706 . . . . . . 7  class  1
1514, 12cfv 4673 . . . . . 6  class  ( w `
 1 )
16 cray2 25519 . . . . . . 7  class ray
175, 16cfv 4673 . . . . . 6  class  (ray `  g )
1813, 15, 17co 5792 . . . . 5  class  ( ( w `  2 ) (ray `  g )
( w `  1
) )
198, 12cfv 4673 . . . . . 6  class  ( w `
 3 )
2013, 19, 17co 5792 . . . . 5  class  ( ( w `  2 ) (ray `  g )
( w `  3
) )
2118, 20cun 3125 . . . 4  class  ( ( ( w `  2
) (ray `  g
) ( w ` 
1 ) )  u.  ( ( w ` 
2 ) (ray `  g ) ( w `
 3 ) ) )
224, 10, 21cmpt 4051 . . 3  class  ( w  e.  ( (PPoints `  g
)dWords 3 )  |->  ( ( ( w ` 
2 ) (ray `  g ) ( w `
 1 ) )  u.  ( ( w `
 2 ) (ray
`  g ) ( w `  3 ) ) ) )
232, 3, 22cmpt 4051 . 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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