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Theorem sbn 1923
 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 1860 . . . 4
21sbbii 1738 . . 3
3 sbnv 1860 . . 3
42, 3bitri 183 . 2
5 ax-17 1506 . . . 4
65hbn 1632 . . 3
76sbco2vh 1916 . 2
85sbco2vh 1916 . . 3
98notbii 657 . 2
104, 7, 93bitr3i 209 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 104  wsb 1735 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736 This theorem is referenced by:  sbcng  2944  difab  3340  rabeq0  3387  abeq0  3388  ssfirab  6815
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