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Theorem slotfn 13475
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 5734 . 2  |-  ( x `
 N )  e. 
_V
2 strfvnd.c . . 3  |-  E  = Slot 
N
3 df-slot 13465 . . 3  |- Slot  N  =  ( x  e.  _V  |->  ( x `  N
) )
42, 3eqtri 2455 . 2  |-  E  =  ( x  e.  _V  |->  ( x `  N
) )
51, 4fnmpti 5565 1  |-  E  Fn  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1652   _Vcvv 2948    e. cmpt 4258    Fn wfn 5441   ` cfv 5446  Slot cslot 13460
This theorem is referenced by:  basfn  27233
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fn 5449  df-fv 5454  df-slot 13465
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