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Theorem biimp3ar 1346
Description: Infer implication from a logical equivalence. Similar to biimpar 297. (Contributed by NM, 2-Jan-2009.)
Hypothesis
Ref Expression
biimp3a.1  |-  ( (
ph  /\  ps )  ->  ( ch  <->  th )
)
Assertion
Ref Expression
biimp3ar  |-  ( (
ph  /\  ps  /\  th )  ->  ch )

Proof of Theorem biimp3ar
StepHypRef Expression
1 biimp3a.1 . . 3  |-  ( (
ph  /\  ps )  ->  ( ch  <->  th )
)
21exbiri 382 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) )
323imp 1193 1  |-  ( (
ph  /\  ps  /\  th )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    <-> wb 105    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  rmoi  3056  brelrng  4858  ssfzo12  10221  abssubge0  11106  qredeu  12091  basgen2  13512  logbprmirr  14321  lgssq  14372  lgssq2  14373
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