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Theorem ecase3d 910
Description: Deduction for elimination by cases. (Contributed by NM, 2-May-1996.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Hypotheses
Ref Expression
ecase3d.1  |-  ( ph  ->  ( ps  ->  th )
)
ecase3d.2  |-  ( ph  ->  ( ch  ->  th )
)
ecase3d.3  |-  ( ph  ->  ( -.  ( ps  \/  ch )  ->  th ) )
Assertion
Ref Expression
ecase3d  |-  ( ph  ->  th )

Proof of Theorem ecase3d
StepHypRef Expression
1 ecase3d.1 . . 3  |-  ( ph  ->  ( ps  ->  th )
)
2 ecase3d.2 . . 3  |-  ( ph  ->  ( ch  ->  th )
)
31, 2jaod 370 . 2  |-  ( ph  ->  ( ( ps  \/  ch )  ->  th )
)
4 ecase3d.3 . 2  |-  ( ph  ->  ( -.  ( ps  \/  ch )  ->  th ) )
53, 4pm2.61d 152 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 358
This theorem is referenced by:  ecased  911  distrlem4pr  8838  atcvat4i  23750  cvrat4  29559
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-or 360
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