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Theorem ecased 910
Description: Deduction for elimination by cases. (Contributed by NM, 8-Oct-2012.)
Hypotheses
Ref Expression
ecased.1  |-  ( ph  ->  ( -.  ps  ->  th ) )
ecased.2  |-  ( ph  ->  ( -.  ch  ->  th ) )
ecased.3  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
Assertion
Ref Expression
ecased  |-  ( ph  ->  th )

Proof of Theorem ecased
StepHypRef Expression
1 ecased.1 . 2  |-  ( ph  ->  ( -.  ps  ->  th ) )
2 ecased.2 . 2  |-  ( ph  ->  ( -.  ch  ->  th ) )
3 pm3.11 485 . . 3  |-  ( -.  ( -.  ps  \/  -.  ch )  ->  ( ps  /\  ch ) )
4 ecased.3 . . 3  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
53, 4syl5 28 . 2  |-  ( ph  ->  ( -.  ( -. 
ps  \/  -.  ch )  ->  th ) )
61, 2, 5ecase3d 909 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357    /\ wa 358
This theorem is referenced by:  ecase3ad  911  itgsplitioo  19208  rolle  19353  dalaw  30697
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 177  df-or 359  df-an 360
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