NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  mp3anl3 GIF version

Theorem mp3anl3 1273
Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
mp3anl3.1 χ
mp3anl3.2 (((φ ψ χ) θ) → τ)
Assertion
Ref Expression
mp3anl3 (((φ ψ) θ) → τ)

Proof of Theorem mp3anl3
StepHypRef Expression
1 mp3anl3.1 . . 3 χ
2 mp3anl3.2 . . . 4 (((φ ψ χ) θ) → τ)
32ex 423 . . 3 ((φ ψ χ) → (θτ))
41, 3mp3an3 1266 . 2 ((φ ψ) → (θτ))
54imp 418 1 (((φ ψ) θ) → τ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  mp3anr3  1276
  Copyright terms: Public domain W3C validator