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Theorem simprbda 375
Description: Deduction eliminating a conjunct. (Contributed by NM, 22-Oct-2007.)
Hypothesis
Ref Expression
pm3.26bda.1  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )
Assertion
Ref Expression
simprbda  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem simprbda
StepHypRef Expression
1 pm3.26bda.1 . . 3  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )
21biimpa 290 . 2  |-  ( (
ph  /\  ps )  ->  ( ch  /\  th ) )
32simpld 110 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  elrabi  2747
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