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Theorem sigaex 27860
 Description: Lemma for issiga 27862 and isrnsiga 27864 The set of sigma algebra with base set is a set. Note: a more generic version with could be useful for sigaval 27861. (Contributed by Thierry Arnoux, 24-Oct-2016.)
Assertion
Ref Expression
sigaex
Distinct variable group:   ,

Proof of Theorem sigaex
StepHypRef Expression
1 df-rab 2823 . . 3
2 selpw 4017 . . . . 5
32anbi1i 695 . . . 4
43abbii 2601 . . 3
51, 4eqtri 2496 . 2
6 vex 3116 . . . 4
7 pwexg 4631 . . . 4
8 pwexg 4631 . . . 4
96, 7, 8mp2b 10 . . 3
109rabex 4598 . 2
115, 10eqeltrri 2552 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 973   wcel 1767  cab 2452  wral 2814  crab 2818  cvv 3113   cdif 3473   wss 3476  cpw 4010  cuni 4245   class class class wbr 4447  com 6685   cdom 7515 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-pow 4625 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2823  df-v 3115  df-in 3483  df-ss 3490  df-pw 4012 This theorem is referenced by:  issiga  27862  isrnsiga  27864
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