Theorem neldifsnd 3798

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

Assertion

Ref	Expression
neldifsnd	|- ( ph -> -. A e. ( B \ { A } ) )

Proof of Theorem neldifsnd

Step	Hyp	Ref	Expression
1		neldifsn 3797	. 2 |- -. A e. ( B \ { A } )
2	1	a1i 9	1 |- ( ph -> -. A e. ( B \ { A } ) )

Syntax hints:   -. wn 3   -> wi 4   e. wcel 2200   \ cdif 3194   {csn 3666

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 617  ax-in2 618  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ne 2401  df-v 2801  df-dif 3199  df-sn 3672

This theorem is referenced by:  difsnb  3810  frirrg  4440  elirr  4632