Theorem nfwrd 11039

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 11012	. 2 |- Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }
2		nfcv 2349	. . . 4 |- F/_ x NN0
3		nfcv 2349	. . . . 5 |- F/_ x w
4		nfcv 2349	. . . . 5 |- F/_ x ( 0..^ l )
5		nfwrd.1	. . . . 5 |- F/_ x S
6	3, 4, 5	nff 5431	. . . 4 |- F/ x w : ( 0..^ l ) --> S
7	2, 6	nfrexw 2546	. . 3 |- F/ x E. l e. NN0 w : ( 0..^ l ) --> S
8	7	nfab 2354	. 2 |- F/_ x { w | E. l e. NN0 w : ( 0..^ l ) --> S }
9	1, 8	nfcxfr 2346	1 |- F/_ xWord S

Syntax hints:   {cab 2192   F/_wnfc 2336   E.wrex 2486   -->wf 5275  (class class class)co 5956   0cc0 7940   NN0cn0 9310  ..^cfzo 10279  Word cword 11011

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-ral 2490  df-rex 2491  df-v 2775  df-un 3174  df-in 3176  df-ss 3183  df-sn 3643  df-pr 3644  df-op 3646  df-br 4051  df-opab 4113  df-rel 4689  df-cnv 4690  df-co 4691  df-dm 4692  df-rn 4693  df-fun 5281  df-fn 5282  df-f 5283  df-word 11012

This theorem is referenced by: (None)