NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  mp3an1i GIF version

Theorem mp3an1i 1270
Description: An inference based on modus ponens. (Contributed by NM, 5-Jul-2005.)
Hypotheses
Ref Expression
mp3an1i.1 ψ
mp3an1i.2 (φ → ((ψ χ θ) → τ))
Assertion
Ref Expression
mp3an1i (φ → ((χ θ) → τ))

Proof of Theorem mp3an1i
StepHypRef Expression
1 mp3an1i.1 . . 3 ψ
2 mp3an1i.2 . . . 4 (φ → ((ψ χ θ) → τ))
32com12 27 . . 3 ((ψ χ θ) → (φτ))
41, 3mp3an1 1264 . 2 ((χ θ) → (φτ))
54com12 27 1 (φ → ((χ 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: (None)
  Copyright terms: Public domain W3C validator