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Definition df-eu 123
 Description: Define the 'exists unique' operator.
Assertion
Ref Expression
df-eu ⊤⊧[∃! = λp:(α → ∗) (λy:α (λx:α [(p:(α → ∗)x:α) = [x:α = y:α]]))]
Distinct variable group:   x,p,y

Detailed syntax breakdown of Definition df-eu
StepHypRef Expression
1 kt 8 . 2 term
2 teu 115 . . 3 term ∃!
3 hal . . . . 5 type α
4 hb 3 . . . . 5 type
53, 4ht 2 . . . 4 type (α → ∗)
6 vp . . . 4 var p
7 tex 113 . . . . 5 term
8 vy . . . . . 6 var y
9 tal 112 . . . . . . 7 term
10 vx . . . . . . . 8 var x
115, 6tv 1 . . . . . . . . . 10 term p:(α → ∗)
123, 10tv 1 . . . . . . . . . 10 term x:α
1311, 12kc 5 . . . . . . . . 9 term (p:(α → ∗)x:α)
143, 8tv 1 . . . . . . . . . 10 term y:α
15 ke 7 . . . . . . . . . 10 term =
1612, 14, 15kbr 9 . . . . . . . . 9 term [x:α = y:α]
1713, 16, 15kbr 9 . . . . . . . 8 term [(p:(α → ∗)x:α) = [x:α = y:α]]
183, 10, 17kl 6 . . . . . . 7 term λx:α [(p:(α → ∗)x:α) = [x:α = y:α]]
199, 18kc 5 . . . . . 6 term (λx:α [(p:(α → ∗)x:α) = [x:α = y:α]])
203, 8, 19kl 6 . . . . 5 term λy:α (λx:α [(p:(α → ∗)x:α) = [x:α = y:α]])
217, 20kc 5 . . . 4 term (λy:α (λx:α [(p:(α → ∗)x:α) = [x:α = y:α]]))
225, 6, 21kl 6 . . 3 term λp:(α → ∗) (λy:α (λx:α [(p:(α → ∗)x:α) = [x:α = y:α]]))
232, 22, 15kbr 9 . 2 term [∃! = λp:(α → ∗) (λy:α (λx:α [(p:(α → ∗)x:α) = [x:α = y:α]]))]
241, 23wffMMJ2 11 1 wff ⊤⊧[∃! = λp:(α → ∗) (λy:α (λx:α [(p:(α → ∗)x:α) = [x:α = y:α]]))]
 Colors of variables: type var term This definition is referenced by:  weu  131  euval  134
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