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Theorem ssneld 3985
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 (𝜑𝐴𝐵)
Assertion
Ref Expression
ssneld (𝜑 → (¬ 𝐶𝐵 → ¬ 𝐶𝐴))

Proof of Theorem ssneld
StepHypRef Expression
1 ssneld.1 . . 3 (𝜑𝐴𝐵)
21sseld 3982 . 2 (𝜑 → (𝐶𝐴𝐶𝐵))
32con3d 152 1 (𝜑 → (¬ 𝐶𝐵 → ¬ 𝐶𝐴))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2107  wss 3949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966
This theorem is referenced by:  ssneldd  3986  kmlem2  10146  hashbclem  14411  prodss  15891  coprmproddvdslem  16599  mrissmrid  17585  mpfrcl  21648  onsuct0  35326  ftc1anc  36569  dvhdimlem  40315  dvh3dim2  40319  dvh3dim3N  40320  mapdh9a  40660  hdmapval0  40704  hdmap11lem2  40713  iundjiunlem  45175  elbigolo1  47243
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