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Theorem unipwr 29019
 Description: A class is a subclass of the union of its power class. This theorem is the right-to-left subclass lemma of unipw 4417. The proof of this theorem was automatically generated from unipwrVD 29018 using a tools command file , translateMWO.cmd , by translating the proof into its non-virtual deduction form and minimizing it. (Contributed by Alan Sare, 25-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
unipwr

Proof of Theorem unipwr
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2961 . . . 4
21snid 3843 . . 3
3 snelpwi 4412 . . 3
4 elunii 4022 . . 3
52, 3, 4sylancr 646 . 2
65ssriv 3354 1
 Colors of variables: wff set class Syntax hints:   wcel 1726   wss 3322  cpw 3801  csn 3816  cuni 4017 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-pw 3803  df-sn 3822  df-pr 3823  df-uni 4018
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