Theorem ssextss 4706

Description: An extensionality-like principle defining subclass in terms of subsets. (Contributed by NM, 30-Jun-2004.)

Assertion

Ref	Expression
ssextss

Distinct variable groups:   ,   ,

Proof of Theorem ssextss

Step	Hyp	Ref	Expression
1		sspwb 4701	. 2
2		dfss2 3492	. 2
3		selpw 4019	. . . 4
4		selpw 4019	. . . 4
5	3, 4	imbi12i 326	. . 3
6	5	albii 1640	. 2
7	1, 2, 6	3bitri 271	1

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

This theorem is referenced by:  ssext  4707  nssss  4708

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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  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-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-pw 4014  df-sn 4030  df-pr 4032