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Theorem nfwrd 11627
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 11610 . 2  |- Word  S  =  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
2 nfcv 2502 . . . 4  |-  F/_ x NN0
3 nfcv 2502 . . . . 5  |-  F/_ x w
4 nfcv 2502 . . . . 5  |-  F/_ x
( 0..^ l )
5 nfwrd.1 . . . . 5  |-  F/_ x S
63, 4, 5nff 5493 . . . 4  |-  F/ x  w : ( 0..^ l ) --> S
72, 6nfrex 2683 . . 3  |-  F/ x E. l  e.  NN0  w : ( 0..^ l ) --> S
87nfab 2506 . 2  |-  F/_ x { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
91, 8nfcxfr 2499 1  |-  F/_ xWord  S
Colors of variables: wff set class
Syntax hints:   {cab 2352   F/_wnfc 2489   E.wrex 2629   -->wf 5354  (class class class)co 5981   0cc0 8884   NN0cn0 10114  ..^cfzo 11025  Word cword 11604
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 937  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-ral 2633  df-rex 2634  df-rab 2637  df-v 2875  df-dif 3241  df-un 3243  df-in 3245  df-ss 3252  df-nul 3544  df-if 3655  df-sn 3735  df-pr 3736  df-op 3738  df-br 4126  df-opab 4180  df-rel 4799  df-cnv 4800  df-co 4801  df-dm 4802  df-rn 4803  df-fun 5360  df-fn 5361  df-f 5362  df-word 11610
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