NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  mpd3an3 GIF version

Theorem mpd3an3 1278
Description: An inference based on modus ponens. (Contributed by NM, 8-Nov-2007.)
Hypotheses
Ref Expression
mpd3an3.2 ((φ ψ) → χ)
mpd3an3.3 ((φ ψ χ) → θ)
Assertion
Ref Expression
mpd3an3 ((φ ψ) → θ)

Proof of Theorem mpd3an3
StepHypRef Expression
1 mpd3an3.2 . 2 ((φ ψ) → χ)
2 mpd3an3.3 . . 3 ((φ ψ χ) → θ)
323expa 1151 . 2 (((φ ψ) χ) → θ)
41, 3mpdan 649 1 ((φ ψ) → θ)
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:  nnsucelr  4428  cupvalg  5812  ovcross  5845  pmvalg  6010  enadj  6060  ovmuc  6130  ovce  6172  addlecncs  6209  leconnnc  6218  ncslesuc  6267
  Copyright terms: Public domain W3C validator