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Theorem biantrud 298
Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 2-Aug-1994.) (Proof shortened by Wolf Lammen, 23-Oct-2013.)
Hypothesis
Ref Expression
biantrud.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
biantrud  |-  ( ph  ->  ( ch  <->  ( ch  /\ 
ps ) ) )

Proof of Theorem biantrud
StepHypRef Expression
1 biantrud.1 . 2  |-  ( ph  ->  ps )
2 iba 294 . 2  |-  ( ps 
->  ( ch  <->  ( ch  /\ 
ps ) ) )
31, 2syl 14 1  |-  ( ph  ->  ( ch  <->  ( ch  /\ 
ps ) ) )
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:  posng  4438  elrnmpt1  4613  fliftf  5470  elxp7  5828  eroveu  6263  reapltxor  7756  divap0b  7838  nnle1eq1  8130  nn0le0eq0  8383  nn0lt10b  8509  ioopos  9049  fz1f1o  10336  nndivdvds  10346  dvdsmultr2  10380
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