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Theorem ecase23d 1286
Description: Variation of ecased 1285 with three disjuncts instead of two. (Contributed by NM, 22-Apr-1994.) (Revised by Jim Kingdon, 9-Dec-2017.)
Hypotheses
Ref Expression
ecase23d.1  |-  ( ph  ->  -.  ch )
ecase23d.2  |-  ( ph  ->  -.  th )
ecase23d.3  |-  ( ph  ->  ( ps  \/  ch  \/  th ) )
Assertion
Ref Expression
ecase23d  |-  ( ph  ->  ps )

Proof of Theorem ecase23d
StepHypRef Expression
1 ecase23d.1 . 2  |-  ( ph  ->  -.  ch )
2 ecase23d.2 . . 3  |-  ( ph  ->  -.  th )
3 ecase23d.3 . . . 4  |-  ( ph  ->  ( ps  \/  ch  \/  th ) )
4 df-3or 925 . . . 4  |-  ( ( ps  \/  ch  \/  th )  <->  ( ( ps  \/  ch )  \/ 
th ) )
53, 4sylib 120 . . 3  |-  ( ph  ->  ( ( ps  \/  ch )  \/  th )
)
62, 5ecased 1285 . 2  |-  ( ph  ->  ( ps  \/  ch ) )
71, 6ecased 1285 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 664    \/ w3o 923
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-3or 925
This theorem is referenced by:  iseqf1olemklt  9879
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