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

Theorem syli 37
Description: Syllogism inference with common nested antecedent. (Contributed by NM, 4-Nov-2004.)
Hypotheses
Ref Expression
syli.1 (𝜓 → (𝜑𝜒))
syli.2 (𝜒 → (𝜑𝜃))
Assertion
Ref Expression
syli (𝜓 → (𝜑𝜃))

Proof of Theorem syli
StepHypRef Expression
1 syli.1 . 2 (𝜓 → (𝜑𝜒))
2 syli.2 . . 3 (𝜒 → (𝜑𝜃))
32com12 30 . 2 (𝜑 → (𝜒𝜃))
41, 3sylcom 28 1 (𝜓 → (𝜑𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  ibd  177  bijadc  852  sbi2v  1848  elab3gf  2807  elreldm  4735  tz6.12c  5419  rntpos  6122  smores  6157  f1domg  6620  negm  9375
  Copyright terms: Public domain W3C validator