ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl2anbr Unicode version

Theorem syl2anbr 292
Description: A double syllogism inference. (Contributed by NM, 29-Jul-1999.)
Hypotheses
Ref Expression
syl2anbr.1  |-  ( ps  <->  ph )
syl2anbr.2  |-  ( ch  <->  ta )
syl2anbr.3  |-  ( ( ps  /\  ch )  ->  th )
Assertion
Ref Expression
syl2anbr  |-  ( (
ph  /\  ta )  ->  th )

Proof of Theorem syl2anbr
StepHypRef Expression
1 syl2anbr.2 . 2  |-  ( ch  <->  ta )
2 syl2anbr.1 . . 3  |-  ( ps  <->  ph )
3 syl2anbr.3 . . 3  |-  ( ( ps  /\  ch )  ->  th )
42, 3sylanbr 285 . 2  |-  ( (
ph  /\  ch )  ->  th )
51, 4sylan2br 288 1  |-  ( (
ph  /\  ta )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    <-> wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  sylancbr  419  tz6.12  5538  ltresr  7816  divmuldivap  8645  fnn0ind  9345  rexanuz  10968  nprmi  12094  cncfval  13692
  Copyright terms: Public domain W3C validator