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Theorem syl2ani 638
Description: A syllogism inference. (Contributed by NM, 3-Aug-1999.)
Hypotheses
Ref Expression
syl2ani.1  |-  ( ph  ->  ch )
syl2ani.2  |-  ( et 
->  th )
syl2ani.3  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
Assertion
Ref Expression
syl2ani  |-  ( ps 
->  ( ( ph  /\  et )  ->  ta )
)

Proof of Theorem syl2ani
StepHypRef Expression
1 syl2ani.1 . 2  |-  ( ph  ->  ch )
2 syl2ani.2 . . 3  |-  ( et 
->  th )
3 syl2ani.3 . . 3  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
42, 3sylan2i 637 . 2  |-  ( ps 
->  ( ( ch  /\  et )  ->  ta )
)
51, 4sylani 636 1  |-  ( ps 
->  ( ( ph  /\  et )  ->  ta )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  frxp  6448  mapen  7263  fin1a2lem9  8278  psss  14636  mgmidmo  14683  aannenlem1  20235  funtransport  25930  cgrxfr  25954  btwnxfr  25955
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361
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