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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 2108  wss 3951
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-clel 2816  df-ss 3968
This theorem is referenced by:  ssneldd  3986  kmlem2  10192  hashbclem  14491  prodss  15983  coprmproddvdslem  16699  mrissmrid  17684  mpfrcl  22109  onsuct0  36442  ftc1anc  37708  dvhdimlem  41446  dvh3dim2  41450  dvh3dim3N  41451  mapdh9a  41791  hdmapval0  41835  hdmap11lem2  41844  iundjiunlem  46474  elbigolo1  48478
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