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Axiom ax-eta 177
 Description: The eta-axiom: a function is determined by its values. (Contributed by Mario Carneiro, 8-Oct-2014.)
Assertion
Ref Expression
ax-eta ⊤⊧(λf:(αβ) [λx:α (f:(αβ)x:α) = f:(αβ)])
Distinct variable group:   x,f

Detailed syntax breakdown of Axiom ax-eta
StepHypRef Expression
1 kt 8 . 2 term
2 tal 122 . . 3 term
3 hal . . . . 5 type α
4 hbe . . . . 5 type β
53, 4ht 2 . . . 4 type (αβ)
6 vf . . . 4 var f
7 vx . . . . . 6 var x
85, 6tv 1 . . . . . . 7 term f:(αβ)
93, 7tv 1 . . . . . . 7 term x:α
108, 9kc 5 . . . . . 6 term (f:(αβ)x:α)
113, 7, 10kl 6 . . . . 5 term λx:α (f:(αβ)x:α)
12 ke 7 . . . . 5 term =
1311, 8, 12kbr 9 . . . 4 term [λx:α (f:(αβ)x:α) = f:(αβ)]
145, 6, 13kl 6 . . 3 term λf:(αβ) [λx:α (f:(αβ)x:α) = f:(αβ)]
152, 14kc 5 . 2 term (λf:(αβ) [λx:α (f:(αβ)x:α) = f:(αβ)])
161, 15wffMMJ2 11 1 wff ⊤⊧(λf:(αβ) [λx:α (f:(αβ)x:α) = f:(αβ)])
 Colors of variables: type var term This axiom is referenced by:  eta  178
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