Theorem nfwrd 11249

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.

Step	Hyp	Ref	Expression
1		df-word 11221	. 2 |- Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }
2		nfcv 2384	. . . 4 |- F/_ x NN0
3		nfcv 2384	. . . . 5 |- F/_ x w
4		nfcv 2384	. . . . 5 |- F/_ x ( 0..^ l )
5		nfwrd.1	. . . . 5 |- F/_ x S
6	3, 4, 5	nff 5504	. . . 4 |- F/ x w : ( 0..^ l ) --> S
7	2, 6	nfrexw 2581	. . 3 |- F/ x E. l e. NN0 w : ( 0..^ l ) --> S
8	7	nfab 2389	. 2 |- F/_ x { w | E. l e. NN0 w : ( 0..^ l ) --> S }
9	1, 8	nfcxfr 2381	1 |- F/_ xWord S

Syntax hints:   {cab 2218   F/_wnfc 2371   E.wrex 2521   -->wf 5347  (class class class)co 6049   0cc0 8126   NN0cn0 9495  ..^cfzo 10475  Word cword 11220

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-ral 2525  df-rex 2526  df-v 2814  df-un 3214  df-in 3216  df-ss 3223  df-sn 3694  df-pr 3695  df-op 3697  df-br 4109  df-opab 4171  df-rel 4755  df-cnv 4756  df-co 4757  df-dm 4758  df-rn 4759  df-fun 5353  df-fn 5354  df-f 5355  df-word 11221

This theorem is referenced by: (None)