NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  mp3an23 GIF version

Theorem mp3an23 1269
Description: An inference based on modus ponens. (Contributed by NM, 14-Jul-2005.)
Hypotheses
Ref Expression
mp3an23.1 ψ
mp3an23.2 χ
mp3an23.3 ((φ ψ χ) → θ)
Assertion
Ref Expression
mp3an23 (φθ)

Proof of Theorem mp3an23
StepHypRef Expression
1 mp3an23.1 . 2 ψ
2 mp3an23.2 . . 3 χ
3 mp3an23.3 . . 3 ((φ ψ χ) → θ)
42, 3mp3an3 1266 . 2 ((φ ψ) → θ)
51, 4mpan2 652 1 (φθ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   w3a 934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  sbciegf  3077  vfintle  4546  vfin1cltv  4547  funpr  5151  enmap2lem5  6067  enprmaplem5  6080  nchoicelem17  6305
  Copyright terms: Public domain W3C validator