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Theorem slotfn 13404
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 5676 . 2  |-  ( x `
 N )  e. 
_V
2 strfvnd.c . . 3  |-  E  = Slot 
N
3 df-slot 13394 . . 3  |- Slot  N  =  ( x  e.  _V  |->  ( x `  N
) )
42, 3eqtri 2401 . 2  |-  E  =  ( x  e.  _V  |->  ( x `  N
) )
51, 4fnmpti 5507 1  |-  E  Fn  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1649   _Vcvv 2893    e. cmpt 4201    Fn wfn 5383   ` cfv 5388  Slot cslot 13389
This theorem is referenced by:  basfn  26928
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2362  ax-sep 4265  ax-nul 4273  ax-pr 4338
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2236  df-mo 2237  df-clab 2368  df-cleq 2374  df-clel 2377  df-nfc 2506  df-ne 2546  df-ral 2648  df-rex 2649  df-rab 2652  df-v 2895  df-sbc 3099  df-dif 3260  df-un 3262  df-in 3264  df-ss 3271  df-nul 3566  df-if 3677  df-sn 3757  df-pr 3758  df-op 3760  df-uni 3952  df-br 4148  df-opab 4202  df-mpt 4203  df-id 4433  df-xp 4818  df-rel 4819  df-cnv 4820  df-co 4821  df-dm 4822  df-iota 5352  df-fun 5390  df-fn 5391  df-fv 5396  df-slot 13394
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