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Theorem nfsb4t 1887
Description: A variable not free remains so after substitution with a distinct variable (closed form of hbsb4 1885). (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 4-Oct-2016.) (Proof rewritten by Jim Kingdon, 9-May-2018.)
Assertion
Ref Expression
nfsb4t  F/  F/

Proof of Theorem nfsb4t
StepHypRef Expression
1 nfnf1 1433 . . . . 5  F/ F/
21nfal 1465 . . . 4  F/ F/
3 nfnae 1607 . . . 4  F/
42, 3nfan 1454 . . 3  F/ F/
5 df-nf 1347 . . . . . 6  F/
65albii 1356 . . . . 5  F/
7 hbsb4t 1886 . . . . 5
86, 7sylbi 114 . . . 4  F/
98imp 115 . . 3  F/
104, 9nfd 1413 . 2  F/  F/
1110ex 108 1  F/  F/
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97  wal 1240   F/wnf 1346  wsb 1642
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643
This theorem is referenced by:  dvelimdf  1889
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