ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  iba Unicode version

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  919  dedlem0a  963  fvopab6  5590  fressnfv  5681  tpostpos  6241  nnmword  6495  unfiexmid  6892  ltmpig  7290  mul0eqap  8577  sup3exmid  8862  xrmaxiflemcom  11201
  Copyright terms: Public domain W3C validator