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Theorem mpii 43
Description: A doubly nested modus ponens inference. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Wolf Lammen, 31-Jul-2012.)
Hypotheses
Ref Expression
mpii.1  |-  ch
mpii.2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
mpii  |-  ( ph  ->  ( ps  ->  th )
)

Proof of Theorem mpii
StepHypRef Expression
1 mpii.1 . . 3  |-  ch
21a1i 11 . 2  |-  ( ps 
->  ch )
3 mpii.2 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
42, 3mpdi 42 1  |-  ( ph  ->  ( ps  ->  th )
)
Colors of variables: wff setvar 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:  intmin  4291  dfiin2g  4348  ssorduni  6594  suceloni  6621  lublecllem  15820  irredmul  17556  opnneiid  19797  isufil2  20578  mdbr3  27417  mdbr4  27418  dmdbr5  27428  filnetlem4  30442
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