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Theorem sbn 1826
 Description: Negation inside and outside of substitution are equivalent. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 3-Feb-2018.)
Assertion
Ref Expression
sbn

Proof of Theorem sbn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbnv 1768 . . . 4
21sbbii 1648 . . 3
3 sbnv 1768 . . 3
42, 3bitri 173 . 2
5 ax-17 1419 . . . 4
65hbn 1544 . . 3
76sbco2v 1821 . 2
85sbco2v 1821 . . 3
98notbii 594 . 2
104, 7, 93bitr3i 199 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 98  wsb 1645 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646 This theorem is referenced by:  sbcng  2803  difab  3206  rabeq0  3247  abeq0  3248
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