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

Theorem sylan9r 390
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 ((θ φ) → (ψτ))

Proof of Theorem sylan9r
StepHypRef Expression
1 sylan9r.1 . . 3 (φ → (ψχ))
2 sylan9r.2 . . 3 (θ → (χτ))
31, 2syl9r 67 . 2 (θ → (φ → (ψτ)))
43imp 115 1 ((θ φ) → (ψτ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem is referenced by:  spimt  1621  sbequi  1717  genpcdl  6502  genpcuu  6503  iccsupr  8565
  Copyright terms: Public domain W3C validator