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Theorem nfwrd 12557
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 12526 . 2  |- Word  S  =  { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
2 nfcv 2616 . . . 4  |-  F/_ x NN0
3 nfcv 2616 . . . . 5  |-  F/_ x w
4 nfcv 2616 . . . . 5  |-  F/_ x
( 0..^ l )
5 nfwrd.1 . . . . 5  |-  F/_ x S
63, 4, 5nff 5709 . . . 4  |-  F/ x  w : ( 0..^ l ) --> S
72, 6nfrex 2917 . . 3  |-  F/ x E. l  e.  NN0  w : ( 0..^ l ) --> S
87nfab 2620 . 2  |-  F/_ x { w  |  E. l  e.  NN0  w : ( 0..^ l ) --> S }
91, 8nfcxfr 2614 1  |-  F/_ xWord  S
Colors of variables: wff setvar class
Syntax hints:   {cab 2439   F/_wnfc 2602   E.wrex 2805   -->wf 5566  (class class class)co 6270   0cc0 9481   NN0cn0 10791  ..^cfzo 11799  Word cword 12518
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2809  df-rex 2810  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-br 4440  df-opab 4498  df-rel 4995  df-cnv 4996  df-co 4997  df-dm 4998  df-rn 4999  df-fun 5572  df-fn 5573  df-f 5574  df-word 12526
This theorem is referenced by: (None)
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