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Theorem mpdi 42
Description: A nested modus ponens deduction. (Contributed by NM, 16-Apr-2005.) (Proof shortened by O'Cat, 15-Jan-2008.)
Hypotheses
Ref Expression
mpdi.1  |-  ( ps 
->  ch )
mpdi.2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
mpdi  |-  ( ph  ->  ( ps  ->  th )
)

Proof of Theorem mpdi
StepHypRef Expression
1 mpdi.1 . . 3  |-  ( ps 
->  ch )
21a1i 9 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
3 mpdi.2 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
42, 3mpdd 40 1  |-  ( ph  ->  ( ps  ->  th )
)
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:  mpii  43  pm2.43d  49  gencbval  2648  sbcimdv  2880  suctr  4184  tfrlem9  5968  lbzbi  8782  flqeqceilz  9400  ndvdsadd  10475  gcdneg  10517  bj-inf2vnlem2  10924
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