Higher-Order Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HOLE Home  >  Th. List  >  df-fo GIF version

Definition df-fo 195
 Description: Define an onto function. (Contributed by Mario Carneiro, 10-Oct-2014.)
Assertion
Ref Expression
df-fo ⊤⊧[onto = λf:(αβ) (λy:β (λx:α [y:β = (f:(αβ)x:α)]))]
Distinct variable group:   x,f,y

Detailed syntax breakdown of Definition df-fo
StepHypRef Expression
1 kt 8 . 2 term
2 tfo 190 . . 3 term onto
3 hal . . . . 5 type α
4 hbe . . . . 5 type β
53, 4ht 2 . . . 4 type (αβ)
6 vf . . . 4 var f
7 tal 122 . . . . 5 term
8 vy . . . . . 6 var y
9 tex 123 . . . . . . 7 term
10 vx . . . . . . . 8 var x
114, 8tv 1 . . . . . . . . 9 term y:β
125, 6tv 1 . . . . . . . . . 10 term f:(αβ)
133, 10tv 1 . . . . . . . . . 10 term x:α
1412, 13kc 5 . . . . . . . . 9 term (f:(αβ)x:α)
15 ke 7 . . . . . . . . 9 term =
1611, 14, 15kbr 9 . . . . . . . 8 term [y:β = (f:(αβ)x:α)]
173, 10, 16kl 6 . . . . . . 7 term λx:α [y:β = (f:(αβ)x:α)]
189, 17kc 5 . . . . . 6 term (λx:α [y:β = (f:(αβ)x:α)])
194, 8, 18kl 6 . . . . 5 term λy:β (λx:α [y:β = (f:(αβ)x:α)])
207, 19kc 5 . . . 4 term (λy:β (λx:α [y:β = (f:(αβ)x:α)]))
215, 6, 20kl 6 . . 3 term λf:(αβ) (λy:β (λx:α [y:β = (f:(αβ)x:α)]))
222, 21, 15kbr 9 . 2 term [onto = λf:(αβ) (λy:β (λx:α [y:β = (f:(αβ)x:α)]))]
231, 22wffMMJ2 11 1 wff ⊤⊧[onto = λf:(αβ) (λy:β (λx:α [y:β = (f:(αβ)x:α)]))]
 Colors of variables: type var term This definition is referenced by: (None)
 Copyright terms: Public domain W3C validator