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Theorem psssstr 3455
 Description: Transitive law for subclass and proper subclass. (Contributed by NM, 3-Apr-1996.)
Assertion
Ref Expression
psssstr

Proof of Theorem psssstr
StepHypRef Expression
1 sspss 3448 . 2
2 psstr 3453 . . . . 5
32ex 425 . . . 4
4 psseq2 3437 . . . . 5
54biimpcd 217 . . . 4
63, 5jaod 371 . . 3
76imp 420 . 2
81, 7sylan2b 463 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   wa 360   wceq 1653   wss 3322   wpss 3323 This theorem is referenced by:  psssstrd  3458  suplem1pr  8934  atexch  23889 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-ne 2603  df-in 3329  df-ss 3336  df-pss 3338
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