Theorem nfwrd 11086

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 11059	. 2 |- Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }
2		nfcv 2372	. . . 4 |- F/_ x NN0
3		nfcv 2372	. . . . 5 |- F/_ x w
4		nfcv 2372	. . . . 5 |- F/_ x ( 0..^ l )
5		nfwrd.1	. . . . 5 |- F/_ x S
6	3, 4, 5	nff 5466	. . . 4 |- F/ x w : ( 0..^ l ) --> S
7	2, 6	nfrexw 2569	. . 3 |- F/ x E. l e. NN0 w : ( 0..^ l ) --> S
8	7	nfab 2377	. 2 |- F/_ x { w | E. l e. NN0 w : ( 0..^ l ) --> S }
9	1, 8	nfcxfr 2369	1 |- F/_ xWord S

Syntax hints:   {cab 2215   F/_wnfc 2359   E.wrex 2509   -->wf 5310  (class class class)co 5994   0cc0 7987   NN0cn0 9357  ..^cfzo 10326  Word cword 11058

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ral 2513  df-rex 2514  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-sn 3672  df-pr 3673  df-op 3675  df-br 4083  df-opab 4145  df-rel 4723  df-cnv 4724  df-co 4725  df-dm 4726  df-rn 4727  df-fun 5316  df-fn 5317  df-f 5318  df-word 11059

This theorem is referenced by: (None)