Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ssiun2s Unicode version

Theorem ssiun2s 3701
 Description: Subset relationship for an indexed union. (Contributed by NM, 26-Oct-2003.)
Hypothesis
Ref Expression
ssiun2s.1
Assertion
Ref Expression
ssiun2s
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ssiun2s
StepHypRef Expression
1 nfcv 2178 . 2
2 nfcv 2178 . . 3
3 nfiu1 3687 . . 3
42, 3nfss 2938 . 2
5 ssiun2s.1 . . 3
65sseq1d 2972 . 2
7 ssiun2 3700 . 2
81, 4, 6, 7vtoclgaf 2618 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393   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: (None)
 Copyright terms: Public domain W3C validator