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Theorem sylan9r 407
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 73 . 2  |-  ( th 
->  ( ph  ->  ( ps  ->  ta ) ) )
43imp 123 1  |-  ( ( th  /\  ph )  ->  ( ps  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem is referenced by:  spimt  1714  sbequi  1811  updjudhf  6957  genpcdl  7320  genpcuu  7321  iccsupr  9742  climuni  11055  tgcn  12366  metrest  12664
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