Theorem exse 4848

Description: Any relation on a set is set-like on it. (Contributed by Mario Carneiro, 22-Jun-2015.)

Assertion

Ref	Expression
exse

Proof of Theorem exse

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		rabexg 4602	. . 3
2	1	ralrimivw 2872	. 2
3		df-se 4844	. 2
4	2, 3	sylibr 212	1

Syntax hints:  ->wi 4  e.wcel 1818  A.wral 2807  {crab 2811  cvv 3109   class class class wbr 4452  Sewse 4841

This theorem is referenced by:  wemoiso  6785  wemoiso2  6786  oiiso  7983  hartogslem1  7988  oemapwe  8134  cantnffval2  8135  oemapweOLD  8156  cantnffval2OLD  8157  om2uzoi  12066  uzsinds  29296  bpolylem  29810

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  ax-sep 4573

This theorem depends on definitions:  df-bi 185  df-or 370  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-ral 2812  df-rab 2816  df-v 3111  df-in 3482  df-ss 3489  df-se 4844