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Axiom ax-eta 165
Description: The eta-axiom: a function is determined by its values.
Assertion
Ref Expression
ax-eta |- T. |= (A.\f:(al -> be) [\x:al (f:(al -> be)x:al) = f:(al -> be)])
Distinct variable group:   x,f

Detailed syntax breakdown of Axiom ax-eta
StepHypRef Expression
1 kt 8 . 2 term T.
2 tal 112 . . 3 term A.
3 hal . . . . 5 type al
4 hbe . . . . 5 type be
53, 4ht 2 . . . 4 type (al -> be)
6 vf . . . 4 var f
7 vx . . . . . 6 var x
85, 6tv 1 . . . . . . 7 term f:(al -> be)
93, 7tv 1 . . . . . . 7 term x:al
108, 9kc 5 . . . . . 6 term (f:(al -> be)x:al)
113, 7, 10kl 6 . . . . 5 term \x:al (f:(al -> be)x:al)
12 ke 7 . . . . 5 term =
1311, 8, 12kbr 9 . . . 4 term [\x:al (f:(al -> be)x:al) = f:(al -> be)]
145, 6, 13kl 6 . . 3 term \f:(al -> be) [\x:al (f:(al -> be)x:al) = f:(al -> be)]
152, 14kc 5 . 2 term (A.\f:(al -> be) [\x:al (f:(al -> be)x:al) = f:(al -> be)])
161, 15wffMMJ2 11 1 wff T. |= (A.\f:(al -> be) [\x:al (f:(al -> be)x:al) = f:(al -> be)])
Colors of variables: type var term
This axiom is referenced by:  eta  166
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