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Theorem psstrd 3454
Description: Proper subclass inclusion is transitive. Deduction form of psstr 3451. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
psstrd.1  |-  ( ph  ->  A  C.  B )
psstrd.2  |-  ( ph  ->  B  C.  C )
Assertion
Ref Expression
psstrd  |-  ( ph  ->  A  C.  C )

Proof of Theorem psstrd
StepHypRef Expression
1 psstrd.1 . 2  |-  ( ph  ->  A  C.  B )
2 psstrd.2 . 2  |-  ( ph  ->  B  C.  C )
3 psstr 3451 . 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. wpss 3321
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 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-ne 2601  df-in 3327  df-ss 3334  df-pss 3336
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