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Theorem 3orit 24066
Description: Closed form of 3ori 1242, (Contributed by Scott Fenton, 20-Apr-2011.)
Assertion
Ref Expression
3orit  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( -. 
ph  /\  -.  ps )  ->  ch ) )

Proof of Theorem 3orit
StepHypRef Expression
1 df-3or 935 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
2 df-or 359 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( -.  ( ph  \/  ps )  ->  ch )
)
3 ioran 476 . . 3  |-  ( -.  ( ph  \/  ps ) 
<->  ( -.  ph  /\  -.  ps ) )
43imbi1i 315 . 2  |-  ( ( -.  ( ph  \/  ps )  ->  ch )  <->  ( ( -.  ph  /\  -.  ps )  ->  ch ) )
51, 2, 43bitri 262 1  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( -. 
ph  /\  -.  ps )  ->  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    \/ wo 357    /\ wa 358    \/ w3o 933
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  df-3or 935
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