Theorem pwss 4027

Description: Subclass relationship for power class. (Contributed by NM, 21-Jun-2009.)

Assertion

Ref	Expression
pwss

Distinct variable groups:   ,   ,

Proof of Theorem pwss

Step	Hyp	Ref	Expression
1		dfss2 3492	. 2
2		selpw 4019	. . . 4
3	2	imbi1i 325	. . 3
4	3	albii 1640	. 2
5	1, 4	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  e.wcel 1818  C_wss 3475  ~Pcpw 4012

This theorem is referenced by:  axpweq  4629  setind2  8187  axgroth5  9223  grothpw  9225  axgroth6  9227

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