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Theorem syl2and 293
Description: A syllogism deduction. (Contributed by NM, 15-Dec-2004.)
Hypotheses
Ref Expression
syl2and.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl2and.2  |-  ( ph  ->  ( th  ->  ta ) )
syl2and.3  |-  ( ph  ->  ( ( ch  /\  ta )  ->  et ) )
Assertion
Ref Expression
syl2and  |-  ( ph  ->  ( ( ps  /\  th )  ->  et )
)

Proof of Theorem syl2and
StepHypRef Expression
1 syl2and.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 syl2and.2 . . 3  |-  ( ph  ->  ( th  ->  ta ) )
3 syl2and.3 . . 3  |-  ( ph  ->  ( ( ch  /\  ta )  ->  et ) )
42, 3sylan2d 292 . 2  |-  ( ph  ->  ( ( ch  /\  th )  ->  et )
)
51, 4syland 291 1  |-  ( ph  ->  ( ( ps  /\  th )  ->  et )
)
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  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anim12d  333  recexprlem1ssl  7448  recexprlem1ssu  7449  xle2add  9669  fzen  9830  bezoutlembi  11699  rpmulgcd2  11782
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