Theorem neldifsn 4321

Description: The class A is not in ( B \ { A } ). (Contributed by David Moews, 1-May-2017.)

Assertion

Ref	Expression
neldifsn	|- -. A e. ( B \ { A } )

Proof of Theorem neldifsn

Step	Hyp	Ref	Expression
1		neirr 2803	. 2 |- -. A =/= A
2		eldifsni 4320	. 2 |- ( A e. ( B \ { A } ) -> A =/= A )
3	1, 2	mto 188	1 |- -. A e. ( B \ { A } )

Syntax hints:   -. wn 3   e. wcel 1990   =/= wne 2794   \ 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:  neldifsnd  4322  fofinf1o  8241  dfac9  8958  xrsupss  12139  fvsetsid  15890  islbs3  19155  islindf4  20177  ufinffr  21733  i1fd  23448  finsumvtxdg2sstep  26445  matunitlindflem1  33405  poimirlem25  33434  itg2addnclem  33461  itg2addnclem2  33462  prter2  34166