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Theorem nan 682
Description: Theorem to move a conjunct in and out of a negation. (Contributed by NM, 9-Nov-2003.)
Assertion
Ref Expression
nan  |-  ( (
ph  ->  -.  ( ps  /\ 
ch ) )  <->  ( ( ph  /\  ps )  ->  -.  ch ) )

Proof of Theorem nan
StepHypRef Expression
1 impexp 261 . 2  |-  ( ( ( ph  /\  ps )  ->  -.  ch )  <->  (
ph  ->  ( ps  ->  -. 
ch ) ) )
2 imnan 680 . . 3  |-  ( ( ps  ->  -.  ch )  <->  -.  ( ps  /\  ch ) )
32imbi2i 225 . 2  |-  ( (
ph  ->  ( ps  ->  -. 
ch ) )  <->  ( ph  ->  -.  ( ps  /\  ch ) ) )
41, 3bitr2i 184 1  |-  ( (
ph  ->  -.  ( ps  /\ 
ch ) )  <->  ( ( ph  /\  ps )  ->  -.  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm4.15  684
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