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Theorem psssstrd 3400
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of psssstr 3397. (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 3397 . 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 3264    C. wpss 3265
This theorem is referenced by:  ackbij1lem15  8048  lsatssn0  29118  lsatexch  29159  lsatcvatlem  29165  lkrpssN  29279
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-ne 2553  df-in 3271  df-ss 3278  df-pss 3280
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