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Theorem prtlem80 26709
Description: Lemma for prter2 26732. (Contributed by Rodolfo Medina, 17-Oct-2010.)
Assertion
Ref Expression
prtlem80  |-  ( A  e.  B  ->  -.  A  e.  ( C  \  { A } ) )

Proof of Theorem prtlem80
StepHypRef Expression
1 neldifsnd 3932 1  |-  ( A  e.  B  ->  -.  A  e.  ( C  \  { A } ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1726    \ cdif 3319   {csn 3816
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-sn 3822
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