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Theorem prtlem80 38862
Description: Lemma for prter2 38882. (Contributed by Rodolfo Medina, 17-Oct-2010.)
Assertion
Ref Expression
prtlem80 (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴}))

Proof of Theorem prtlem80
StepHypRef Expression
1 neldifsnd 4793 1 (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴}))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2108  cdif 3948  {csn 4626
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  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-v 3482  df-dif 3954  df-sn 4627
This theorem is referenced by: (None)
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