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Theorem sbn 1954
 Description: Negation inside and outside of substitution are equivalent. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbn

Proof of Theorem sbn
StepHypRef Expression
1 sbequ2 1890 . . . . 5
2 sbequ2 1890 . . . . 5
31, 2nsyld 134 . . . 4
43a4s 1700 . . 3
5 sb4 1945 . . . 4
6 sb1 1887 . . . . . 6
7 equs3 1627 . . . . . 6
86, 7sylib 190 . . . . 5
98con2i 114 . . . 4
105, 9syl6 31 . . 3
114, 10pm2.61i 158 . 2
12 sbequ1 1889 . . . 4
1312con3rr3 130 . . 3
14 sb2 1888 . . . . . 6
15 notnot 284 . . . . . . 7
1615sbbii 1885 . . . . . 6
1714, 16sylibr 205 . . . . 5
1817con3i 129 . . . 4
19 equs3 1627 . . . 4
2018, 19sylibr 205 . . 3
21 df-sb 1883 . . 3
2213, 20, 21sylanbrc 648 . 2
2311, 22impbii 182 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wb 178   wa 360  wal 1532  wex 1537  wsb 1882 This theorem is referenced by:  sbi2  1956  sbor  1958  sban  1961  a4sbe  1967  sb8e  1987  sbex  2088  sbcng  2961  difab  3344  pm13.196a  26781  compneOLD  26810 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883
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