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Theorem sylan9r 402
Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
sylan9r.1  |-  ( ph  ->  ( ps  ->  ch ) )
sylan9r.2  |-  ( th 
->  ( ch  ->  ta ) )
Assertion
Ref Expression
sylan9r  |-  ( ( th  /\  ph )  ->  ( ps  ->  ta ) )

Proof of Theorem sylan9r
StepHypRef Expression
1 sylan9r.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
2 sylan9r.2 . . 3  |-  ( th 
->  ( ch  ->  ta ) )
31, 2syl9r 72 . 2  |-  ( th 
->  ( ph  ->  ( ps  ->  ta ) ) )
43imp 122 1  |-  ( ( th  /\  ph )  ->  ( ps  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem is referenced by:  spimt  1671  sbequi  1767  updjudhf  6768  genpcdl  7076  genpcuu  7077  iccsupr  9382  climuni  10677
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