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Theorem imdistanda 437
Description: Distribution of implication with conjunction (deduction version with conjoined antecedent). (Contributed by Jeff Madsen, 19-Jun-2011.)
Hypothesis
Ref Expression
imdistanda.1  |-  ( (
ph  /\  ps )  ->  ( ch  ->  th )
)
Assertion
Ref Expression
imdistanda  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ps 
/\  th ) ) )

Proof of Theorem imdistanda
StepHypRef Expression
1 imdistanda.1 . . 3  |-  ( (
ph  /\  ps )  ->  ( ch  ->  th )
)
21ex 113 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32imdistand 436 1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ps 
/\  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
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:  fzind  8595  uzss  8772  exbtwnzlemshrink  9387  rebtwn2zlemshrink  9392  cau3lem  10201
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