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Theorem ssextss 3947
Description: An extensionality-like principle defining subclass in terms of subsets. (Contributed by NM, 30-Jun-2004.)
Assertion
Ref Expression
ssextss 
C_  C_ 
C_
Distinct variable groups:   ,   ,

Proof of Theorem ssextss
StepHypRef Expression
1 sspwb 3943 . 2 
C_  ~P  C_ 
~P
2 dfss2 2928 . 2  ~P  C_  ~P 
~P  ~P
3 vex 2554 . . . . 5 
_V
43elpw 3357 . . . 4  ~P  C_
53elpw 3357 . . . 4  ~P  C_
64, 5imbi12i 228 . . 3  ~P  ~P  C_  C_
76albii 1356 . 2  ~P  ~P  C_ 
C_
81, 2, 73bitri 195 1 
C_  C_ 
C_
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   wcel 1390    C_ wss 2911   ~Pcpw 3351
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373
This theorem is referenced by:  ssext  3948  nssssr  3949
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