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Theorem mpdd 41
Description: A nested modus ponens deduction. (Contributed by NM, 12-Dec-2004.)
Hypotheses
Ref Expression
mpdd.1  |-  ( ph  ->  ( ps  ->  ch ) )
mpdd.2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
mpdd  |-  ( ph  ->  ( ps  ->  th )
)

Proof of Theorem mpdd
StepHypRef Expression
1 mpdd.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 mpdd.2 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32a2d 26 . 2  |-  ( ph  ->  ( ( ps  ->  ch )  ->  ( ps  ->  th ) ) )
41, 3mpd 13 1  |-  ( ph  ->  ( ps  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  mpid  42  mpdi  43  syld  45  syl6c  66  mpteqb  5608  oprabid  5909  nnmordi  6519  nnmord  6520  brecop  6627  findcard2  6891  findcard2s  6892  ordiso2  7036  zindd  9373  cau3lem  11125  climcau  11357  dvdsabseq  11855  metrest  14045  bj-charfunr  14601
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