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Theorem slotfn 16493
 Description: A slot is a function on sets, treated as structures. (Contributed by Mario Carneiro, 22-Sep-2015.)
Hypothesis
Ref Expression
strfvnd.c 𝐸 = Slot 𝑁
Assertion
Ref Expression
slotfn 𝐸 Fn V

Proof of Theorem slotfn
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 fvex 6676 . 2 (𝑥𝑁) ∈ V
2 strfvnd.c . . 3 𝐸 = Slot 𝑁
3 df-slot 16479 . . 3 Slot 𝑁 = (𝑥 ∈ V ↦ (𝑥𝑁))
42, 3eqtri 2842 . 2 𝐸 = (𝑥 ∈ V ↦ (𝑥𝑁))
51, 4fnmpti 6484 1 𝐸 Fn V
 Colors of variables: wff setvar class Syntax hints:   = wceq 1531  Vcvv 3493   ↦ cmpt 5137   Fn wfn 6343  ‘cfv 6348  Slot cslot 16474 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2154  ax-12 2170  ax-ext 2791  ax-sep 5194  ax-nul 5201  ax-pr 5320 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1084  df-tru 1534  df-ex 1775  df-nf 1779  df-sb 2064  df-mo 2616  df-eu 2648  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-ral 3141  df-rex 3142  df-rab 3145  df-v 3495  df-sbc 3771  df-dif 3937  df-un 3939  df-in 3941  df-ss 3950  df-nul 4290  df-if 4466  df-sn 4560  df-pr 4562  df-op 4566  df-uni 4831  df-br 5058  df-opab 5120  df-mpt 5138  df-id 5453  df-xp 5554  df-rel 5555  df-cnv 5556  df-co 5557  df-dm 5558  df-iota 6307  df-fun 6350  df-fn 6351  df-fv 6356  df-slot 16479 This theorem is referenced by:  basfn  16495
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