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Theorem psssstrd 3448
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of psssstr 3445. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
psssstrd.1  |-  ( ph  ->  A  C.  B )
psssstrd.2  |-  ( ph  ->  B  C_  C )
Assertion
Ref Expression
psssstrd  |-  ( ph  ->  A  C.  C )

Proof of Theorem psssstrd
StepHypRef Expression
1 psssstrd.1 . 2  |-  ( ph  ->  A  C.  B )
2 psssstrd.2 . 2  |-  ( ph  ->  B  C_  C )
3 psssstr 3445 . 2  |-  ( ( A  C.  B  /\  B  C_  C )  ->  A  C.  C )
41, 2, 3syl2anc 643 1  |-  ( ph  ->  A  C.  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 3312    C. wpss 3313
This theorem is referenced by:  ackbij1lem15  8106  lsatssn0  29737  lsatexch  29778  lsatcvatlem  29784  lkrpssN  29898
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-ne 2600  df-in 3319  df-ss 3326  df-pss 3328
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