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Theorem simplbiim 379
Description: Implication from an eliminated conjunct equivalent to the antecedent. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
simplbiim.1  |-  ( ph  <->  ( ps  /\  ch )
)
simplbiim.2  |-  ( ch 
->  th )
Assertion
Ref Expression
simplbiim  |-  ( ph  ->  th )

Proof of Theorem simplbiim
StepHypRef Expression
1 simplbiim.1 . 2  |-  ( ph  <->  ( ps  /\  ch )
)
2 simplbiim.2 . . 3  |-  ( ch 
->  th )
32adantl 271 . 2  |-  ( ( ps  /\  ch )  ->  th )
41, 3sylbi 119 1  |-  ( ph  ->  th )
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  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  zltaddlt1le  9104  oddnn02np1  10424
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