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Theorem slotfn 16202
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 6424 . 2 (𝑥𝑁) ∈ V
2 strfvnd.c . . 3 𝐸 = Slot 𝑁
3 df-slot 16188 . . 3 Slot 𝑁 = (𝑥 ∈ V ↦ (𝑥𝑁))
42, 3eqtri 2821 . 2 𝐸 = (𝑥 ∈ V ↦ (𝑥𝑁))
51, 4fnmpti 6233 1 𝐸 Fn V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1653  Vcvv 3385  cmpt 4922   Fn wfn 6096  cfv 6101  Slot cslot 16183
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777  ax-sep 4975  ax-nul 4983  ax-pr 5097
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-3an 1110  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-mo 2591  df-eu 2609  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-ral 3094  df-rex 3095  df-rab 3098  df-v 3387  df-sbc 3634  df-dif 3772  df-un 3774  df-in 3776  df-ss 3783  df-nul 4116  df-if 4278  df-sn 4369  df-pr 4371  df-op 4375  df-uni 4629  df-br 4844  df-opab 4906  df-mpt 4923  df-id 5220  df-xp 5318  df-rel 5319  df-cnv 5320  df-co 5321  df-dm 5322  df-iota 6064  df-fun 6103  df-fn 6104  df-fv 6109  df-slot 16188
This theorem is referenced by:  basfn  16204  bascnvimaeqv  17075
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