ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syld3an2 GIF version

Theorem syld3an2 1193
Description: A syllogism inference. (Contributed by NM, 20-May-2007.)
Hypotheses
Ref Expression
syld3an2.1 ((𝜑𝜒𝜃) → 𝜓)
syld3an2.2 ((𝜑𝜓𝜃) → 𝜏)
Assertion
Ref Expression
syld3an2 ((𝜑𝜒𝜃) → 𝜏)

Proof of Theorem syld3an2
StepHypRef Expression
1 syld3an2.1 . . . 4 ((𝜑𝜒𝜃) → 𝜓)
213com23 1121 . . 3 ((𝜑𝜃𝜒) → 𝜓)
3 syld3an2.2 . . . 4 ((𝜑𝜓𝜃) → 𝜏)
433com23 1121 . . 3 ((𝜑𝜃𝜓) → 𝜏)
52, 4syld3an3 1191 . 2 ((𝜑𝜃𝜒) → 𝜏)
653com23 1121 1 ((𝜑𝜒𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  nppcan2  7305  nnncan  7309  nnncan2  7311  ltdivmul  7917  ledivmul  7918  ltdiv23  7933  lediv23  7934  dvdssub2  10149
  Copyright terms: Public domain W3C validator