Theorem nfwrd 10942

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 10915	. 2 |- Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }
2		nfcv 2336	. . . 4 |- F/_ x NN0
3		nfcv 2336	. . . . 5 |- F/_ x w
4		nfcv 2336	. . . . 5 |- F/_ x ( 0..^ l )
5		nfwrd.1	. . . . 5 |- F/_ x S
6	3, 4, 5	nff 5400	. . . 4 |- F/ x w : ( 0..^ l ) --> S
7	2, 6	nfrexw 2533	. . 3 |- F/ x E. l e. NN0 w : ( 0..^ l ) --> S
8	7	nfab 2341	. 2 |- F/_ x { w | E. l e. NN0 w : ( 0..^ l ) --> S }
9	1, 8	nfcxfr 2333	1 |- F/_ xWord S

Syntax hints:   {cab 2179   F/_wnfc 2323   E.wrex 2473   -->wf 5250  (class class class)co 5918   0cc0 7872   NN0cn0 9240  ..^cfzo 10208  Word cword 10914

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-rex 2478  df-v 2762  df-un 3157  df-in 3159  df-ss 3166  df-sn 3624  df-pr 3625  df-op 3627  df-br 4030  df-opab 4091  df-rel 4666  df-cnv 4667  df-co 4668  df-dm 4669  df-rn 4670  df-fun 5256  df-fn 5257  df-f 5258  df-word 10915

This theorem is referenced by: (None)