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Theorem nfsb4t 2130
 Description: A variable not free remains so after substitution with a distinct variable (closed form of nfsb4 2131). (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 4-Oct-2016.) (Proof shortened by Wolf Lammen, 11-May-2018.)
Assertion
Ref Expression
nfsb4t

Proof of Theorem nfsb4t
StepHypRef Expression
1 sbequ12 1992 . . . . . . . 8
21sps 1865 . . . . . . 7
32drnf2 2072 . . . . . 6
43biimpd 207 . . . . 5
54spsd 1867 . . . 4
65impcom 430 . . 3
76a1d 25 . 2
8 nfnf1 1899 . . . . 5
98nfal 1947 . . . 4
10 nfnae 2058 . . . 4
119, 10nfan 1928 . . 3
12 nfa1 1897 . . . 4
13 nfnae 2058 . . . 4
1412, 13nfan 1928 . . 3
15 sp 1859 . . . 4
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  F/wnf 1616  [wsb 1739 This theorem is referenced by:  nfsb4  2131  nfsbd  2186 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740