Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sspwimpcf Unicode version

Theorem sspwimpcf 28886
 Description: If a class is a subclass of another class, then its power class is a subclass of that other class's power class. Left-to-right implication of Exercise 18 of [TakeutiZaring] p. 18. sspwimpcf 28886, using conventional notation, was translated from its virtual deduction form, sspwimpcfVD 28887, using a translation program. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sspwimpcf

Proof of Theorem sspwimpcf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2951 . . . . . 6
2 id 20 . . . . . . 7
3 id 20 . . . . . . . 8
4 elpwi 3799 . . . . . . . 8
53, 4syl 16 . . . . . . 7
6 sstr2 3347 . . . . . . . 8
76impcom 420 . . . . . . 7
82, 5, 7syl2an 464 . . . . . 6
9 elpwg 3798 . . . . . . 7
109biimpar 472 . . . . . 6
111, 8, 10eel021old 28655 . . . . 5
1211ex 424 . . . 4
1312alrimiv 1641 . . 3
14 dfss2 3329 . . . 4
1514biimpri 198 . . 3
1613, 15syl 16 . 2
1716iin1 28517 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549   wcel 1725  cvv 2948   wss 3312  cpw 3791 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326  df-pw 3793
 Copyright terms: Public domain W3C validator