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Theorem ecase3ad 911
Description: Deduction for elimination by cases. (Contributed by NM, 24-May-2013.)
Hypotheses
Ref Expression
ecase3ad.1  |-  ( ph  ->  ( ps  ->  th )
)
ecase3ad.2  |-  ( ph  ->  ( ch  ->  th )
)
ecase3ad.3  |-  ( ph  ->  ( ( -.  ps  /\ 
-.  ch )  ->  th )
)
Assertion
Ref Expression
ecase3ad  |-  ( ph  ->  th )

Proof of Theorem ecase3ad
StepHypRef Expression
1 notnot2 104 . . 3  |-  ( -. 
-.  ps  ->  ps )
2 ecase3ad.1 . . 3  |-  ( ph  ->  ( ps  ->  th )
)
31, 2syl5 28 . 2  |-  ( ph  ->  ( -.  -.  ps  ->  th ) )
4 notnot2 104 . . 3  |-  ( -. 
-.  ch  ->  ch )
5 ecase3ad.2 . . 3  |-  ( ph  ->  ( ch  ->  th )
)
64, 5syl5 28 . 2  |-  ( ph  ->  ( -.  -.  ch  ->  th ) )
7 ecase3ad.3 . 2  |-  ( ph  ->  ( ( -.  ps  /\ 
-.  ch )  ->  th )
)
83, 6, 7ecased 910 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358
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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