Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  iunss Unicode version

Theorem iunss 3698
 Description: Subset theorem for an indexed union. (Contributed by NM, 13-Sep-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
iunss
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iunss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 3659 . . 3
21sseq1i 2969 . 2
3 abss 3009 . 2
4 dfss2 2934 . . . 4
54ralbii 2330 . . 3
6 ralcom4 2576 . . 3
7 r19.23v 2425 . . . 4
87albii 1359 . . 3
95, 6, 83bitrri 196 . 2
102, 3, 93bitri 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wcel 1393  cab 2026  wral 2306  wrex 2307   wss 2917  ciun 3657 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-iun 3659 This theorem is referenced by:  iunss2  3702  djussxp  4481  fun11iun  5147
 Copyright terms: Public domain W3C validator