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Theorem nfwrd 12535
Description: Hypothesis builder for Word  S. (Contributed by Mario Carneiro, 26-Feb-2016.)
Hypothesis
Ref Expression
nfwrd.1  |-  F/_ x S
Assertion
Ref Expression
nfwrd  |-  F/_ xWord  S

Proof of Theorem nfwrd
Dummy variables  w  l are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-word 12508 . 2  |- Word  S  =  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
2 nfcv 2629 . . . 4  |-  F/_ x NN0
3 nfcv 2629 . . . . 5  |-  F/_ x w
4 nfcv 2629 . . . . 5  |-  F/_ x
( 0..^ l )
5 nfwrd.1 . . . . 5  |-  F/_ x S
63, 4, 5nff 5727 . . . 4  |-  F/ x  w : ( 0..^ l ) --> S
72, 6nfrex 2927 . . 3  |-  F/ x E. l  e.  NN0  w : ( 0..^ l ) --> S
87nfab 2633 . 2  |-  F/_ x { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
91, 8nfcxfr 2627 1  |-  F/_ xWord  S
Colors of variables: wff setvar class
Syntax hints:   {cab 2452   F/_wnfc 2615   E.wrex 2815   -->wf 5584  (class class class)co 6284   0cc0 9492   NN0cn0 10795  ..^cfzo 11792  Word cword 12500
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-rn 5010  df-fun 5590  df-fn 5591  df-f 5592  df-word 12508
This theorem is referenced by: (None)
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