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Theorem pwunim 4137
 Description: The power class of the union of two classes equals the union of their power classes, iff one class is a subclass of the other. Part of Exercise 7(b) of [Enderton] p. 28. (Contributed by Jim Kingdon, 30-Sep-2018.)
Assertion
Ref Expression
pwunim

Proof of Theorem pwunim
StepHypRef Expression
1 pwssunim 4135 . . 3
2 pwunss 4134 . . . 4
32biantru 297 . . 3
41, 3sylib 121 . 2
5 eqss 3054 . 2
64, 5sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wo 667   wceq 1296   cun 3011   wss 3013  cpw 3449 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-v 2635  df-un 3017  df-in 3019  df-ss 3026  df-pw 3451 This theorem is referenced by: (None)
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