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Theorem imim12d 74
Description: Deduction combining antecedents and consequents. (Contributed by NM, 7-Aug-1994.) (Proof shortened by O'Cat, 30-Oct-2011.)
Hypotheses
Ref Expression
imim12d.1  |-  ( ph  ->  ( ps  ->  ch ) )
imim12d.2  |-  ( ph  ->  ( th  ->  ta ) )
Assertion
Ref Expression
imim12d  |-  ( ph  ->  ( ( ch  ->  th )  ->  ( ps  ->  ta ) ) )

Proof of Theorem imim12d
StepHypRef Expression
1 imim12d.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 imim12d.2 . . 3  |-  ( ph  ->  ( th  ->  ta ) )
32imim2d 54 . 2  |-  ( ph  ->  ( ( ch  ->  th )  ->  ( ch  ->  ta ) ) )
41, 3syl5d 68 1  |-  ( ph  ->  ( ( ch  ->  th )  ->  ( ps  ->  ta ) ) )
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:  imim1d  75  equveli  1732  hbsb4t  1988  mo23  2040  rspcimdv  2790  r19.29uz  10771  txlm  12458  metcnpi3  12696  addcncntoplem  12730  cnplimcim  12815  setindis  13195  bdsetindis  13197  bj-findis  13207
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