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Theorem imim12d 73
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 53 . 2  |-  ( ph  ->  ( ( ch  ->  th )  ->  ( ch  ->  ta ) ) )
41, 3syl5d 67 1  |-  ( ph  ->  ( ( ch  ->  th )  ->  ( ps  ->  ta ) ) )
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:  imim1d  74  equveli  1683  hbsb4t  1931  mo23  1983  rspcimdv  2703  r19.29uz  10016  setindis  10920  bdsetindis  10922  bj-findis  10932
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