ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sylan9r GIF version

Theorem sylan9r 396
Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
sylan9r.1 (𝜑 → (𝜓𝜒))
sylan9r.2 (𝜃 → (𝜒𝜏))
Assertion
Ref Expression
sylan9r ((𝜃𝜑) → (𝜓𝜏))

Proof of Theorem sylan9r
StepHypRef Expression
1 sylan9r.1 . . 3 (𝜑 → (𝜓𝜒))
2 sylan9r.2 . . 3 (𝜃 → (𝜒𝜏))
31, 2syl9r 71 . 2 (𝜃 → (𝜑 → (𝜓𝜏)))
43imp 119 1 ((𝜃𝜑) → (𝜓𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104
This theorem is referenced by:  spimt  1640  sbequi  1736  genpcdl  6675  genpcuu  6676  iccsupr  8936  climuni  10045
  Copyright terms: Public domain W3C validator