Theorem nfwrd 11335

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 11307	. 2 |- Word S = { w | E. l e. NN0 w : ( 0..^ l ) --> S }
2		nfcv 2392	. . . 4 |- F/_ x NN0
3		nfcv 2392	. . . . 5 |- F/_ x w
4		nfcv 2392	. . . . 5 |- F/_ x ( 0..^ l )
5		nfwrd.1	. . . . 5 |- F/_ x S
6	3, 4, 5	nff 5530	. . . 4 |- F/ x w : ( 0..^ l ) --> S
7	2, 6	nfrexw 2589	. . 3 |- F/ x E. l e. NN0 w : ( 0..^ l ) --> S
8	7	nfab 2397	. 2 |- F/_ x { w | E. l e. NN0 w : ( 0..^ l ) --> S }
9	1, 8	nfcxfr 2389	1 |- F/_ xWord S

This proof depends on syntax axioms:   {cab 2224   F/_wnfc 2379   E.wrex 2529   -->wf 5373  (class class class)co 6085   0cc0 8179   NN0cn0 9565  ..^cfzo 10551  Word cword 11306

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-ral 2533  df-rex 2534  df-v 2823  df-un 3224  df-in 3226  df-ss 3233  df-sn 3715  df-pr 3716  df-op 3718  df-br 4131  df-opab 4193  df-rel 4781  df-cnv 4782  df-co 4783  df-dm 4784  df-rn 4785  df-fun 5379  df-fn 5380  df-f 5381  df-word 11307

This theorem is used by: (None)