Theorem nfwrd 11146

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 11118	. 2 |- Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }
2		nfcv 2374	. . . 4 |- F/_ x NN0
3		nfcv 2374	. . . . 5 |- F/_ x w
4		nfcv 2374	. . . . 5 |- F/_ x ( 0..^ l )
5		nfwrd.1	. . . . 5 |- F/_ x S
6	3, 4, 5	nff 5479	. . . 4 |- F/ x w : ( 0..^ l ) --> S
7	2, 6	nfrexw 2571	. . 3 |- F/ x E. l e. NN0 w : ( 0..^ l ) --> S
8	7	nfab 2379	. 2 |- F/_ x { w | E. l e. NN0 w : ( 0..^ l ) --> S }
9	1, 8	nfcxfr 2371	1 |- F/_ xWord S

Syntax hints:   {cab 2217   F/_wnfc 2361   E.wrex 2511   -->wf 5322  (class class class)co 6018   0cc0 8032   NN0cn0 9402  ..^cfzo 10377  Word cword 11117

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3an 1006  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-ral 2515  df-rex 2516  df-v 2804  df-un 3204  df-in 3206  df-ss 3213  df-sn 3675  df-pr 3676  df-op 3678  df-br 4089  df-opab 4151  df-rel 4732  df-cnv 4733  df-co 4734  df-dm 4735  df-rn 4736  df-fun 5328  df-fn 5329  df-f 5330  df-word 11118

This theorem is referenced by: (None)