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

Theorem sbss 3329
 Description: Set substitution into the first argument of a subset relation. (Contributed by Rodolfo Medina, 7-Jul-2010.) (Proof shortened by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
sbss
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem sbss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2560 . 2
2 sbequ 1721 . 2
3 sseq1 2966 . 2
4 nfv 1421 . . 3
5 sseq1 2966 . . 3
64, 5sbie 1674 . 2
71, 2, 3, 6vtoclb 2611 1
 Colors of variables: wff set class Syntax hints:   wb 98  wsb 1645   wss 2917 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-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-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559  df-in 2924  df-ss 2931 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator