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Theorem syl8 70
Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994.) (Proof shortened by Wolf Lammen, 3-Aug-2012.)
Hypotheses
Ref Expression
syl8.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
syl8.2  |-  ( th 
->  ta )
Assertion
Ref Expression
syl8  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )

Proof of Theorem syl8
StepHypRef Expression
1 syl8.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 syl8.2 . . 3  |-  ( th 
->  ta )
32a1i 9 . 2  |-  ( ph  ->  ( th  ->  ta ) )
41, 3syl6d 69 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  com45  88  syl8ib  164  imp5a  350  con4biddc  788  3exp  1138  suctr  4184  ssorduni  4239  nneneq  6392  qreccl  8808  bj-inf2vnlem2  10924
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