ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm4.45im Unicode version

Theorem pm4.45im 327
Description: Conjunction with implication. Compare Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 17-May-1998.)
Assertion
Ref Expression
pm4.45im  |-  ( ph  <->  (
ph  /\  ( ps  ->  ph ) ) )

Proof of Theorem pm4.45im
StepHypRef Expression
1 ax-1 5 . . 3  |-  ( ph  ->  ( ps  ->  ph )
)
21ancli 316 . 2  |-  ( ph  ->  ( ph  /\  ( ps  ->  ph ) ) )
3 simpl 107 . 2  |-  ( (
ph  /\  ( ps  ->  ph ) )  ->  ph )
42, 3impbii 124 1  |-  ( ph  <->  (
ph  /\  ( ps  ->  ph ) ) )
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:  difdif  3125
  Copyright terms: Public domain W3C validator