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

Theorem syl2anbr 288
Description: A double syllogism inference. (Contributed by NM, 29-Jul-1999.)
Hypotheses
Ref Expression
syl2anbr.1 (𝜓𝜑)
syl2anbr.2 (𝜒𝜏)
syl2anbr.3 ((𝜓𝜒) → 𝜃)
Assertion
Ref Expression
syl2anbr ((𝜑𝜏) → 𝜃)

Proof of Theorem syl2anbr
StepHypRef Expression
1 syl2anbr.2 . 2 (𝜒𝜏)
2 syl2anbr.1 . . 3 (𝜓𝜑)
3 syl2anbr.3 . . 3 ((𝜓𝜒) → 𝜃)
42, 3sylanbr 281 . 2 ((𝜑𝜒) → 𝜃)
51, 4sylan2br 284 1 ((𝜑𝜏) → 𝜃)
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:  sylancbr  413  tz6.12  5415  ltresr  7611  divmuldivap  8432  fnn0ind  9118  rexanuz  10700  nprmi  11701  cncfval  12623
  Copyright terms: Public domain W3C validator