Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  eldifpw Structured version   Unicode version

Theorem eldifpw 6611
 Description: Membership in a power class difference. (Contributed by NM, 25-Mar-2007.)
Hypothesis
Ref Expression
eldifpw.1
Assertion
Ref Expression
eldifpw

Proof of Theorem eldifpw
StepHypRef Expression
1 elpwi 4024 . . . 4
2 unss1 3669 . . . . 5
3 eldifpw.1 . . . . . . 7
4 unexg 6600 . . . . . . 7
53, 4mpan2 671 . . . . . 6
6 elpwg 4023 . . . . . 6
75, 6syl 16 . . . . 5
82, 7syl5ibr 221 . . . 4
91, 8mpd 15 . . 3
10 elpwi 4024 . . . . 5
1110unssbd 3678 . . . 4
1211con3i 135 . . 3
139, 12anim12i 566 . 2
14 eldif 3481 . 2
1513, 14sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 369   wcel 1819  cvv 3109   cdif 3468   cun 3469   wss 3471  cpw 4015 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-8 1821  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695  ax-un 6591 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rex 2813  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-pw 4017  df-sn 4033  df-pr 4035  df-uni 4252 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator