Theorem pwuni 4683

Description: A class is a subclass of the power class of its union. Exercise 6(b) of [Enderton] p. 38. (Contributed by NM, 14-Oct-1996.)

Assertion

Ref	Expression
pwuni

Proof of Theorem pwuni

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		elssuni 4279	. . 3
2		selpw 4019	. . 3
3	1, 2	sylibr 212	. 2
4	3	ssriv 3507	1

Syntax hints:  e.wcel 1818  C_wss 3475  ~Pcpw 4012  U.cuni 4249

This theorem is referenced by:  uniexb  6610  fipwuni  7906  uniwf  8258  rankuni  8302  rankc2  8310  rankxplim  8318  fin23lem17  8739  axcclem  8858  grurn  9200  istopon  19426  eltg3i  19462  cmpfi  19908  hmphdis  20297  ptcmpfi  20314  fbssfi  20338  mopnfss  20946  shsspwh  26164  circtopn  27840  hasheuni  28091  issgon  28123  sigaclci  28132  sigagenval  28140  dmsigagen  28144  imambfm  28233

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-v 3111  df-in 3482  df-ss 3489  df-pw 4014  df-uni 4250