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Theorem mp2d 47
Description: A double modus ponens deduction. (Contributed by NM, 23-May-2013.) (Proof shortened by Wolf Lammen, 23-Jul-2013.)
Hypotheses
Ref Expression
mp2d.1  |-  ( ph  ->  ps )
mp2d.2  |-  ( ph  ->  ch )
mp2d.3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
mp2d  |-  ( ph  ->  th )

Proof of Theorem mp2d
StepHypRef Expression
1 mp2d.1 . 2  |-  ( ph  ->  ps )
2 mp2d.2 . . 3  |-  ( ph  ->  ch )
3 mp2d.3 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
42, 3mpid 42 . 2  |-  ( ph  ->  ( ps  ->  th )
)
51, 4mpd 13 1  |-  ( ph  ->  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:  fisseneq  6905  prloc  7440  axcaucvglemres  7848  bezoutlemmain  11940  coprm  12085  sqrt2irr  12103  oddprmdvds  12293  xblss2ps  13119  xblss2  13120  lgsprme0  13658  pw1nct  13958  apdiff  14002
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