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Theorem pm2.86d 93
Description: Deduction based on pm2.86 94. (Contributed by NM, 29-Jun-1995.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)
Hypothesis
Ref Expression
pm2.86d.1  |-  ( ph  ->  ( ( ps  ->  ch )  ->  ( ps  ->  th ) ) )
Assertion
Ref Expression
pm2.86d  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )

Proof of Theorem pm2.86d
StepHypRef Expression
1 ax-1 5 . . 3  |-  ( ch 
->  ( ps  ->  ch ) )
2 pm2.86d.1 . . 3  |-  ( ph  ->  ( ( ps  ->  ch )  ->  ( ps  ->  th ) ) )
31, 2syl5 28 . 2  |-  ( ph  ->  ( ch  ->  ( ps  ->  th ) ) )
43com23 72 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  pm2.86  94  pm5.74  235  ax12olem6  1873  ax15  1961  a12study2  29134
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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