Theorem rexdifsn 4159

Description: Restricted existential quantification over a set with an element removed. (Contributed by NM, 4-Feb-2015.)

Assertion

Ref	Expression
rexdifsn

Proof of Theorem rexdifsn

Step	Hyp	Ref	Expression
1		eldifsn 4155	. . . 4
2	1	anbi1i 695	. . 3
3		anass 649	. . 3
4	2, 3	bitri 249	. 2
5	4	rexbii2 2957	1

Syntax hints:  <->wb 184  /\wa 369  e.wcel 1818  =/=wne 2652  E.wrex 2808  \cdif 3472  {csn 4029

This theorem is referenced by:  symgfix2  16441  2spot2iun2spont  24891  usgra2pth0  32355  dihatexv  37065  lcfl8b  37231

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rex 2813  df-v 3111  df-dif 3478  df-sn 4030