Theorem pwssb 4417

Description: Two ways to express a collection of subclasses. (Contributed by NM, 19-Jul-2006.)

Assertion

Ref	Expression
pwssb

Distinct variable groups:   ,   ,

Proof of Theorem pwssb

Step	Hyp	Ref	Expression
1		sspwuni 4416	. 2
2		unissb 4281	. 2
3	1, 2	bitri 249	1

Syntax hints:  <->wb 184  A.wral 2807  C_wss 3475  ~Pcpw 4012  U.cuni 4249

This theorem is referenced by:  istps5OLD  19425  ustuni  20729  metustfbasOLD  21068  metustfbas  21069  dmvlsiga  28129  1stmbfm  28231  2ndmbfm  28232  dya2iocucvr  28255

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-ral 2812  df-v 3111  df-in 3482  df-ss 3489  df-pw 4014  df-uni 4250