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Theorem simplbiim 384
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 275 . 2  |-  ( ( ps  /\  ch )  ->  th )
41, 3sylbi 120 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> 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
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mpodifsnif  5864  ixpm  6624  finct  7001  apsscn  8416  zltaddlt1le  9796  oddnn02np1  11584
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