ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl6rbb GIF version

Theorem syl6rbb 195
Description: A syllogism inference from two biconditionals. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
syl6rbb.1 (𝜑 → (𝜓𝜒))
syl6rbb.2 (𝜒𝜃)
Assertion
Ref Expression
syl6rbb (𝜑 → (𝜃𝜓))

Proof of Theorem syl6rbb
StepHypRef Expression
1 syl6rbb.1 . . 3 (𝜑 → (𝜓𝜒))
2 syl6rbb.2 . . 3 (𝜒𝜃)
31, 2syl6bb 194 . 2 (𝜑 → (𝜓𝜃))
43bicomd 139 1 (𝜑 → (𝜃𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  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:  syl6rbbr  197  bibif  649  pm5.61  743  oranabs  764  pm5.7dc  900  nbbndc  1330  resopab2  4746  xpcom  4964  f1od2  5982  map1  6509  ac6sfi  6594  elznn0  8735  rexuz3  10388
  Copyright terms: Public domain W3C validator