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Theorem psstrd 3296
Description: Proper subclass inclusion is transitive. Deduction form of psstr 3293. (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 3293 . 2  |-  ( ( A  C.  B  /\  B  C.  C )  ->  A  C.  C )
41, 2, 3syl2anc 642 1  |-  ( ph  ->  A  C.  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C. wpss 3166
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-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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