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Theorem ssneld 3444
 Description: If a class is not in another class, it is also not in a subclass of that class. Deduction form. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
ssneld.1
Assertion
Ref Expression
ssneld

Proof of Theorem ssneld
StepHypRef Expression
1 ssneld.1 . . 3
21sseld 3441 . 2
32con3d 133 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wcel 1842   wss 3414 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-in 3421  df-ss 3428 This theorem is referenced by:  ssneldd  3445  kmlem2  8563  hashbclem  12550  prodss  13906  mrissmrid  15255  mpfrcl  18507  onsuct0  30673  ftc1anc  31471  dvhdimlem  34464  dvh3dim2  34468  dvh3dim3N  34469  mapdh9a  34810  hdmapval0  34856  hdmap11lem2  34865  elbigolo1  38688
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