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Theorem iunssf 37500
 Description: Subset theorem for an indexed union. (Contributed by Glauco Siliprandi, 3-Mar-2021.)
Hypothesis
Ref Expression
iunssf.1
Assertion
Ref Expression
iunssf

Proof of Theorem iunssf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 4271 . . 3
21sseq1i 3442 . 2
3 abss 3484 . 2
4 dfss2 3407 . . . 4
54ralbii 2823 . . 3
6 ralcom4 3052 . . 3
7 nfcv 2612 . . . . . 6
8 iunssf.1 . . . . . 6
97, 8nfel 2624 . . . . 5
109r19.23 2862 . . . 4
1110albii 1699 . . 3
125, 6, 113bitrri 280 . 2
132, 3, 123bitri 279 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  wal 1450   wcel 1904  cab 2457  wnfc 2599  wral 2756  wrex 2757   wss 3390  ciun 4269 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-v 3033  df-in 3397  df-ss 3404  df-iun 4271 This theorem is referenced by:  iunmapss  37568
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