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Axiom ax-ac 196
 Description: Defining property of the indefinite descriptor: it selects an element from any type. This is equivalent to global choice in ZF. (Contributed by Mario Carneiro, 10-Oct-2014.)
Assertion
Ref Expression
ax-ac ⊤⊧(λp:(α → ∗) (λx:α [(p:(α → ∗)x:α) ⇒ (p:(α → ∗)(εp:(α → ∗)))]))
Distinct variable group:   x,p

Detailed syntax breakdown of Axiom ax-ac
StepHypRef Expression
1 kt 8 . 2 term
2 tal 122 . . 3 term
3 hal . . . . 5 type α
4 hb 3 . . . . 5 type
53, 4ht 2 . . . 4 type (α → ∗)
6 vp . . . 4 var p
7 vx . . . . . 6 var x
85, 6tv 1 . . . . . . . 8 term p:(α → ∗)
93, 7tv 1 . . . . . . . 8 term x:α
108, 9kc 5 . . . . . . 7 term (p:(α → ∗)x:α)
11 tat 191 . . . . . . . . 9 term ε
1211, 8kc 5 . . . . . . . 8 term p:(α → ∗))
138, 12kc 5 . . . . . . 7 term (p:(α → ∗)(εp:(α → ∗)))
14 tim 121 . . . . . . 7 term
1510, 13, 14kbr 9 . . . . . 6 term [(p:(α → ∗)x:α) ⇒ (p:(α → ∗)(εp:(α → ∗)))]
163, 7, 15kl 6 . . . . 5 term λx:α [(p:(α → ∗)x:α) ⇒ (p:(α → ∗)(εp:(α → ∗)))]
172, 16kc 5 . . . 4 term (λx:α [(p:(α → ∗)x:α) ⇒ (p:(α → ∗)(εp:(α → ∗)))])
185, 6, 17kl 6 . . 3 term λp:(α → ∗) (λx:α [(p:(α → ∗)x:α) ⇒ (p:(α → ∗)(εp:(α → ∗)))])
192, 18kc 5 . 2 term (λp:(α → ∗) (λx:α [(p:(α → ∗)x:α) ⇒ (p:(α → ∗)(εp:(α → ∗)))]))
201, 19wffMMJ2 11 1 wff ⊤⊧(λp:(α → ∗) (λx:α [(p:(α → ∗)x:α) ⇒ (p:(α → ∗)(εp:(α → ∗)))]))
 Colors of variables: type var term This axiom is referenced by:  ac  197
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