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Theorem nfsb4t 1906
 Description: A variable not free remains so after substitution with a distinct variable (closed form of hbsb4 1904). (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

Proof of Theorem nfsb4t
StepHypRef Expression
1 nfnf1 1452 . . . . 5
21nfal 1484 . . . 4
3 nfnae 1626 . . . 4
42, 3nfan 1473 . . 3
5 df-nf 1366 . . . . . 6
65albii 1375 . . . . 5
7 hbsb4t 1905 . . . . 5
86, 7sylbi 118 . . . 4
98imp 119 . . 3
104, 9nfd 1432 . 2
1110ex 112 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 101  wal 1257  wnf 1365  wsb 1661 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265  df-nf 1366  df-sb 1662 This theorem is referenced by:  dvelimdf  1908
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