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Theorem pwssunim 4021
 Description: The power class of the union of two classes is a subset of the union of their power classes, if one class is a subclass of the other. One direction of Exercise 4.12(l) of [Mendelson] p. 235. (Contributed by Jim Kingdon, 30-Sep-2018.)
Assertion
Ref Expression
pwssunim

Proof of Theorem pwssunim
StepHypRef Expression
1 ssequn2 3116 . . . . 5
2 pweq 3362 . . . . . 6
3 eqimss 2997 . . . . . 6
42, 3syl 14 . . . . 5
51, 4sylbi 114 . . . 4
6 ssequn1 3113 . . . . 5
7 pweq 3362 . . . . . 6
8 eqimss 2997 . . . . . 6
97, 8syl 14 . . . . 5
106, 9sylbi 114 . . . 4
115, 10orim12i 676 . . 3
1211orcoms 649 . 2
13 ssun 3122 . 2
1412, 13syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 629   wceq 1243   cun 2915   wss 2917  cpw 3359 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361 This theorem is referenced by:  pwunim  4023
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