NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  pm2.27 GIF version

Theorem pm2.27 35
Description: This theorem, called "Assertion," can be thought of as closed form of modus ponens ax-mp 8. Theorem *2.27 of [WhiteheadRussell] p. 104. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pm2.27 (φ → ((φψ) → ψ))

Proof of Theorem pm2.27
StepHypRef Expression
1 id 19 . 2 ((φψ) → (φψ))
21com12 27 1 (φ → ((φψ) → ψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
This theorem is referenced by:  pm2.43  47  com23  72  pm3.2im  137  mth8  138  biimt  325  pm3.35  570  pm2.26  853  dvelimv  1939  ax10lem6  1943  ax10o  1952  ax10-16  2190  ax10o-o  2203  eqfnfv  5392  dff3  5420  weds  5938  ncssfin  6151  nclenn  6249
  Copyright terms: Public domain W3C validator