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Theorem sspwimp 28884
 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. sspwimp 28884, using conventional notation, was translated from virtual deduction form, sspwimpVD 28885, using a translation program. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sspwimp

Proof of Theorem sspwimp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2951 . . . . . . 7
21a1i 11 . . . . . 6
3 id 20 . . . . . . 7
4 id 20 . . . . . . . 8
5 elpwi 3799 . . . . . . . 8
64, 5syl 16 . . . . . . 7
7 sstr 3348 . . . . . . . 8
87ancoms 440 . . . . . . 7
93, 6, 8syl2an 464 . . . . . 6
102, 9elpwgded 28506 . . . . . 6
112, 9, 10uun0.1 28744 . . . . 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   wa 359   wtru 1325  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
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