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Theorem sylan9ssr 3022
Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004.)
Hypotheses
Ref Expression
sylan9ssr.1  |-  ( ph  ->  A  C_  B )
sylan9ssr.2  |-  ( ps 
->  B  C_  C )
Assertion
Ref Expression
sylan9ssr  |-  ( ( ps  /\  ph )  ->  A  C_  C )

Proof of Theorem sylan9ssr
StepHypRef Expression
1 sylan9ssr.1 . . 3  |-  ( ph  ->  A  C_  B )
2 sylan9ssr.2 . . 3  |-  ( ps 
->  B  C_  C )
31, 2sylan9ss 3021 . 2  |-  ( (
ph  /\  ps )  ->  A  C_  C )
43ancoms 264 1  |-  ( ( ps  /\  ph )  ->  A  C_  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    C_ wss 2982
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-in 2988  df-ss 2995
This theorem is referenced by:  intssuni2m  3680
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