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Theorem iunpwss 4055
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssiun 4008 . . 3
2 eliun 3973 . . . 4
3 vex 2862 . . . . . 6
43elpw 3728 . . . . 5
54rexbii 2639 . . . 4
62, 5bitri 240 . . 3
73elpw 3728 . . . 4
8 uniiun 4019 . . . . 5
98sseq2i 3296 . . . 4
107, 9bitri 240 . . 3
111, 6, 103imtr4i 257 . 2
1211ssriv 3277 1
 Colors of variables: wff setvar class Syntax hints:   wcel 1710  wrex 2615   wss 3257  cpw 3722  cuni 3891  ciun 3969 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pw 3724  df-uni 3892  df-iun 3971 This theorem is referenced by: (None)
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