Theorem prtlem80 34146

Description: Lemma for prter2 34166. (Contributed by Rodolfo Medina, 17-Oct-2010.)

Assertion

Ref	Expression
prtlem80	|- ( A e. B -> -. A e. ( C \ { A } ) )

Proof of Theorem prtlem80

Step	Hyp	Ref	Expression
1		neldifsnd 4322	1 |- ( A e. B -> -. A e. ( C \ { A } ) )

Syntax hints:   -. wn 3   -> wi 4   e. wcel 1990   \ cdif 3571   {csn 4177

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ne 2795  df-v 3202  df-dif 3577  df-sn 4178

This theorem is referenced by: (None)