Mathbox for Frédéric Liné < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  untindd Unicode version

Theorem untindd 25122
 Description: An "induction principle" for until, roughly stating that it is the least fixed point satisfying a property like ax-ltl5 25096. (Contributed by Mario Carneiro, 30-Aug-2016.)
Hypotheses
Ref Expression
untindd.1
untindd.2
Assertion
Ref Expression
untindd

Proof of Theorem untindd
StepHypRef Expression
1 untindd.1 . . . 4
2 untindd.2 . . . 4
31, 2jaoi 368 . . 3
43ax-lmp 25081 . 2
5 untind 25121 . 2
64, 5ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 357   wa 358  wbox 25073  wcirc 25075   wunt 25076 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 25077  ax-ltl2 25078  ax-ltl3 25079  ax-ltl4 25080  ax-lmp 25081  ax-nmp 25082  ax-ltl5 25096  ax-ltl6 25097 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 25083
 Copyright terms: Public domain W3C validator