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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 |- T. |= (A.\p:(al -> *) (A.\x:al [(p:(al -> *)x:al) ==> (p:(al -> *)(@p:(al -> *)))]))
Distinct variable group:   x,p

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