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Theorem nfwrd 11426
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 11409 . 2  |- Word  S  =  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
2 nfcv 2419 . . . 4  |-  F/_ x NN0
3 nfcv 2419 . . . . 5  |-  F/_ x w
4 nfcv 2419 . . . . 5  |-  F/_ x
( 0..^ l )
5 nfwrd.1 . . . . 5  |-  F/_ x S
63, 4, 5nff 5387 . . . 4  |-  F/ x  w : ( 0..^ l ) --> S
72, 6nfrex 2598 . . 3  |-  F/ x E. l  e.  NN0  w : ( 0..^ l ) --> S
87nfab 2423 . 2  |-  F/_ x { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
91, 8nfcxfr 2416 1  |-  F/_ xWord  S
Colors of variables: wff set class
Syntax hints:   {cab 2269   F/_wnfc 2406   E.wrex 2544   -->wf 5251  (class class class)co 5858   0cc0 8737   NN0cn0 9965  ..^cfzo 10870  Word cword 11403
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-fun 5257  df-fn 5258  df-f 5259  df-word 11409
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