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Theorem prtlem80 37373
Description: Lemma for prter2 37393. (Contributed by Rodolfo Medina, 17-Oct-2010.)
Assertion
Ref Expression
prtlem80 (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴}))

Proof of Theorem prtlem80
StepHypRef Expression
1 neldifsnd 4757 1 (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴}))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2107  cdif 3911  {csn 4590
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-ne 2941  df-v 3449  df-dif 3917  df-sn 4591
This theorem is referenced by: (None)
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