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Theorem sbn 2015
 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 1640 . . . . 5
2 sbequ2 1640 . . . . 5
31, 2nsyld 132 . . . 4
43sps 1751 . . 3
5 sb4 2006 . . . 4
6 sb1 1641 . . . . . 6
7 equs3 1634 . . . . . 6
86, 7sylib 188 . . . . 5
98con2i 112 . . . 4
105, 9syl6 29 . . 3
114, 10pm2.61i 156 . 2
12 sbequ1 1871 . . . 4
1312con3rr3 128 . . 3
14 sb2 1976 . . . . . 6
15 notnot 282 . . . . . . 7
1615sbbii 1643 . . . . . 6
1714, 16sylibr 203 . . . . 5
1817con3i 127 . . . 4
19 equs3 1634 . . . 4
2018, 19sylibr 203 . . 3
21 df-sb 1639 . . 3
2213, 20, 21sylanbrc 645 . 2
2311, 22impbii 180 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1530  wex 1531  wsb 1638 This theorem is referenced by:  sbi2  2017  sbor  2019  sban  2022  spsbe  2028  sb8e  2046  sbex  2080  sbcng  3044  difab  3450  pm13.196a  27717  compneOLD  27746 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639
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