ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mp2ani Structured version   GIF version

Theorem mp2ani 408
Description: An inference based on modus ponens. (Contributed by NM, 12-Dec-2004.)
Hypotheses
Ref Expression
mp2ani.1 ψ
mp2ani.2 χ
mp2ani.3 (φ → ((ψ χ) → θ))
Assertion
Ref Expression
mp2ani (φθ)

Proof of Theorem mp2ani
StepHypRef Expression
1 mp2ani.2 . 2 χ
2 mp2ani.1 . . 3 ψ
3 mp2ani.3 . . 3 (φ → ((ψ χ) → θ))
42, 3mpani 406 . 2 (φ → (χθ))
51, 4mpi 15 1 (φθ)
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  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  th3q  6147  addnnnq0  6432  mulnnnq0  6433  addsrpr  6673  mulsrpr  6674
  Copyright terms: Public domain W3C validator