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Theorem dedt 923
Description: The weak deduction theorem. For more information, see the Deduction Theorem link on the Metamath Proof Explorer home page. (Contributed by NM, 26-Jun-2002.)
Hypotheses
Ref Expression
dedt.1  |-  ( (
ph 
<->  ( ( ph  /\  ch )  \/  ( ps  /\  -.  ch )
) )  ->  ( th 
<->  ta ) )
dedt.2  |-  ta
Assertion
Ref Expression
dedt  |-  ( ch 
->  th )

Proof of Theorem dedt
StepHypRef Expression
1 dedlema 920 . 2  |-  ( ch 
->  ( ph  <->  ( ( ph  /\  ch )  \/  ( ps  /\  -.  ch ) ) ) )
2 dedt.2 . . 3  |-  ta
3 dedt.1 . . 3  |-  ( (
ph 
<->  ( ( ph  /\  ch )  \/  ( ps  /\  -.  ch )
) )  ->  ( th 
<->  ta ) )
42, 3mpbiri 224 . 2  |-  ( (
ph 
<->  ( ( ph  /\  ch )  \/  ( ps  /\  -.  ch )
) )  ->  th )
51, 4syl 15 1  |-  ( ch 
->  th )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  con3th  924
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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