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Theorem sspsstr 3294
 Description: Transitive law for subclass and proper subclass. (Contributed by NM, 3-Apr-1996.)
Assertion
Ref Expression
sspsstr

Proof of Theorem sspsstr
StepHypRef Expression
1 sspss 3288 . 2
2 psstr 3293 . . . . 5
32ex 423 . . . 4
4 psseq1 3276 . . . . 5
54biimprd 214 . . . 4
63, 5jaoi 368 . . 3
76imp 418 . 2
81, 7sylanb 458 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 357   wa 358   wceq 1632   wss 3165   wpss 3166 This theorem is referenced by:  sspsstrd  3297  ordtr2  4452  php  7061  marypha1lem  7202  ackbij1lem15  7876  fin23lem38  7991  canthp1lem2  8291  ltexprlem2  8677  suplem1pr  8692  fbfinnfr  17552  ppiltx  20431 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-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-ne 2461  df-in 3172  df-ss 3179  df-pss 3181
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