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Theorem nssssr 3949
Description: Negation of subclass relationship. Compare nssr 2997. (Contributed by Jim Kingdon, 17-Sep-2018.)
Assertion
Ref Expression
nssssr (x(xA ¬ xB) → ¬ AB)
Distinct variable groups:   x,A   x,B

Proof of Theorem nssssr
StepHypRef Expression
1 exanaliim 1535 . 2 (x(xA ¬ xB) → ¬ x(xAxB))
2 ssextss 3947 . 2 (ABx(xAxB))
31, 2sylnibr 601 1 (x(xA ¬ xB) → ¬ AB)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97  wal 1240  wex 1378  wss 2911
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373
This theorem is referenced by: (None)
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