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Theorem simplbi2 377
Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011.)
Hypothesis
Ref Expression
pm3.26bi2.1  |-  ( ph  <->  ( ps  /\  ch )
)
Assertion
Ref Expression
simplbi2  |-  ( ps 
->  ( ch  ->  ph )
)

Proof of Theorem simplbi2
StepHypRef Expression
1 pm3.26bi2.1 . . 3  |-  ( ph  <->  ( ps  /\  ch )
)
21biimpri 131 . 2  |-  ( ( ps  /\  ch )  ->  ph )
32ex 113 1  |-  ( ps 
->  ( ch  ->  ph )
)
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:  pm5.62dc  887  pm5.63dc  888  simplbi2com  1374  reuss2  3251  elni2  6566  elfz0ubfz0  9213  elfzmlbp  9220  fzo1fzo0n0  9269  elfzo0z  9270  fzofzim  9274  elfzodifsumelfzo  9287  dfgcd2  10547  ialgcvga  10577
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