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Theorem sbss 3659
 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 2862 . 2
2 sbequ 2060 . 2
3 sseq1 3292 . 2
4 nfv 1619 . . 3
5 sseq1 3292 . . 3
64, 5sbie 2038 . 2
71, 2, 3, 6vtoclb 2912 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wsb 1648   wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by: (None)
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