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Theorem sbcss12g 23157
 Description: Set substitution into the both argument of a subset relation. (Contributed by Thierry Arnoux, 25-Jan-2017.)
Assertion
Ref Expression
sbcss12g
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbcss12g
StepHypRef Expression
1 nfcsb1v 3126 . . 3
2 nfcsb1v 3126 . . 3
31, 2nfss 3186 . 2
4 csbeq1a 3102 . . 3
5 csbeq1a 3102 . . 3
64, 5sseq12d 3220 . 2
73, 6sbciegf 3035 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wceq 1632   wcel 1696  wsbc 3004  csb 3094   wss 3165 This theorem is referenced by:  iuninc  23174 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-v 2803  df-sbc 3005  df-csb 3095  df-in 3172  df-ss 3179
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