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Theorem nfwrd 11778
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 11761 . 2  |- Word  S  =  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
2 nfcv 2579 . . . 4  |-  F/_ x NN0
3 nfcv 2579 . . . . 5  |-  F/_ x w
4 nfcv 2579 . . . . 5  |-  F/_ x
( 0..^ l )
5 nfwrd.1 . . . . 5  |-  F/_ x S
63, 4, 5nff 5624 . . . 4  |-  F/ x  w : ( 0..^ l ) --> S
72, 6nfrex 2768 . . 3  |-  F/ x E. l  e.  NN0  w : ( 0..^ l ) --> S
87nfab 2583 . 2  |-  F/_ x { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
91, 8nfcxfr 2576 1  |-  F/_ xWord  S
Colors of variables: wff set class
Syntax hints:   {cab 2429   F/_wnfc 2566   E.wrex 2713   -->wf 5485  (class class class)co 6117   0cc0 9028   NN0cn0 10259  ..^cfzo 11173  Word cword 11755
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ral 2717  df-rex 2718  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3768  df-sn 3849  df-pr 3850  df-op 3852  df-br 4244  df-opab 4298  df-rel 4920  df-cnv 4921  df-co 4922  df-dm 4923  df-rn 4924  df-fun 5491  df-fn 5492  df-f 5493  df-word 11761
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