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Theorem sbcng 2949
 Description: Move negation in and out of class substitution. (Contributed by NM, 16-Jan-2004.)
Assertion
Ref Expression
sbcng

Proof of Theorem sbcng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 2912 . 2
2 dfsbcq2 2912 . . 3
32notbid 656 . 2
4 sbn 1925 . 2
51, 3, 4vtoclbg 2747 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 104   wceq 1331   wcel 1480  wsb 1735  wsbc 2909 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-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sbc 2910 This theorem is referenced by:  sbcn1  2956  sbcnel12g  3019  sbcne12g  3020  difopab  4672  zsupcllemstep  11644
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