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Theorem mpbi2and 861
Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 6-Nov-2011.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)
Hypotheses
Ref Expression
mpbi2and.1  |-  ( ph  ->  ps )
mpbi2and.2  |-  ( ph  ->  ch )
mpbi2and.3  |-  ( ph  ->  ( ( ps  /\  ch )  <->  th ) )
Assertion
Ref Expression
mpbi2and  |-  ( ph  ->  th )

Proof of Theorem mpbi2and
StepHypRef Expression
1 mpbi2and.1 . . 3  |-  ( ph  ->  ps )
2 mpbi2and.2 . . 3  |-  ( ph  ->  ch )
31, 2jca 294 . 2  |-  ( ph  ->  ( ps  /\  ch ) )
4 mpbi2and.3 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  <->  th ) )
53, 4mpbid 139 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    <-> wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  supisoti  6414  remim  9688  resqrtcl  9856  divalgmod  10239  oddpwdclemxy  10257
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