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Theorem iba 298
Description: Introduction of antecedent as conjunct. Theorem *4.73 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-Mar-1994.) (Revised by NM, 24-Mar-2013.)
Assertion
Ref Expression
iba  |-  ( ph  ->  ( ps  <->  ( ps  /\ 
ph ) ) )

Proof of Theorem iba
StepHypRef Expression
1 pm3.21 262 . 2  |-  ( ph  ->  ( ps  ->  ( ps  /\  ph ) ) )
2 simpl 108 . 2  |-  ( ( ps  /\  ph )  ->  ps )
31, 2impbid1 141 1  |-  ( ph  ->  ( ps  <->  ( ps  /\ 
ph ) ) )
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:  biantru  300  biantrud  302  ancrb  320  rbaibd  909  dedlem0a  952  fvopab6  5510  fressnfv  5600  tpostpos  6154  nnmword  6407  unfiexmid  6799  ltmpig  7140  mul0eqap  8424  sup3exmid  8708  xrmaxiflemcom  11011
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