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Theorem slotfn 17064
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 6859 . 2 (𝑥𝑁) ∈ V
2 strfvnd.c . . 3 𝐸 = Slot 𝑁
3 df-slot 17062 . . 3 Slot 𝑁 = (𝑥 ∈ V ↦ (𝑥𝑁))
42, 3eqtri 2761 . 2 𝐸 = (𝑥 ∈ V ↦ (𝑥𝑁))
51, 4fnmpti 6648 1 𝐸 Fn V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  Vcvv 3447  cmpt 5192   Fn wfn 6495  cfv 6500  Slot cslot 17061
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5260  ax-nul 5267  ax-pr 5388
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2535  df-eu 2564  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3407  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-if 4491  df-sn 4591  df-pr 4593  df-op 4597  df-uni 4870  df-br 5110  df-opab 5172  df-mpt 5193  df-id 5535  df-xp 5643  df-rel 5644  df-cnv 5645  df-co 5646  df-dm 5647  df-iota 6452  df-fun 6502  df-fn 6503  df-fv 6508  df-slot 17062
This theorem is referenced by:  basfn  17095  bj-isrvec  35815
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