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

Theorem sylanbr 279
Description: A syllogism inference. (Contributed by NM, 18-May-1994.)
Hypotheses
Ref Expression
sylanbr.1  |-  ( ps  <->  ph )
sylanbr.2  |-  ( ( ps  /\  ch )  ->  th )
Assertion
Ref Expression
sylanbr  |-  ( (
ph  /\  ch )  ->  th )

Proof of Theorem sylanbr
StepHypRef Expression
1 sylanbr.1 . . 3  |-  ( ps  <->  ph )
21biimpri 131 . 2  |-  ( ph  ->  ps )
3 sylanbr.2 . 2  |-  ( ( ps  /\  ch )  ->  th )
42, 3sylan 277 1  |-  ( (
ph  /\  ch )  ->  th )
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:  syl2anbr  286  mosubt  2778  xpiindim  4521  funfvdm  5288  caovimo  5745  tfrlem7  5986  iinerm  6265  expclzaplem  9649  expgt0  9658  expge0  9661  expge1  9662  rplpwr  10623
  Copyright terms: Public domain W3C validator