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Theorem iunpwss 3889
 Description: Inclusion of an indexed union of a power class in the power class of the union of its index. Part of Exercise 24(b) of [Enderton] p. 33. (Contributed by NM, 25-Nov-2003.)
Assertion
Ref Expression
iunpwss
Distinct variable group:   ,

Proof of Theorem iunpwss
StepHypRef Expression
1 ssiun 3842 . . 3
2 eliun 3807 . . . 4
3 vex 2730 . . . . . 6
43elpw 3536 . . . . 5
54rexbii 2532 . . . 4
62, 5bitri 242 . . 3
73elpw 3536 . . . 4
8 uniiun 3853 . . . . 5
98sseq2i 3124 . . . 4
107, 9bitri 242 . . 3
111, 6, 103imtr4i 259 . 2
1211ssriv 3105 1
 Colors of variables: wff set class Syntax hints:   wcel 1621  wrex 2510   wss 3078  cpw 3530  cuni 3727  ciun 3803 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rex 2514  df-v 2729  df-in 3085  df-ss 3089  df-pw 3532  df-uni 3728  df-iun 3805
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