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Theorem clsslem 13060
 Description: The closure of a subclass is a subclass of the closure. (Contributed by RP, 16-May-2020.)
Assertion
Ref Expression
clsslem
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem clsslem
StepHypRef Expression
1 sstr2 3441 . . . 4
21anim1d 568 . . 3
32ss2abdv 3504 . 2
4 intss 4258 . 2
53, 4syl 17 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371  cab 2439   wss 3406  cint 4237 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ral 2744  df-in 3413  df-ss 3420  df-int 4238 This theorem is referenced by:  trclsslem  13066
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