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Theorem untind 25121
 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.)
Assertion
Ref Expression
untind

Proof of Theorem untind
StepHypRef Expression
1 simpr 447 . . 3
2 ax-ltl5 25096 . . . . . . . 8
3 ax-ltl3 25079 . . . . . . . . . . 11
43anim2d 548 . . . . . . . . . 10
54orim2d 813 . . . . . . . . 9
6 alneal1 25103 . . . . . . . . 9
75, 6sylan9r 639 . . . . . . . 8
82, 7syl5bi 208 . . . . . . 7
98ex 423 . . . . . 6
109boxrim 25110 . . . . 5
1110adantr 451 . . . 4
12 ax-ltl6 25097 . . . . 5
13 orc 374 . . . . . . . . 9
1413, 6syl5 28 . . . . . . . 8
1514a1dd 42 . . . . . . 7
1615diaimd 25113 . . . . . 6
1716imp 418 . . . . 5
1812, 17sylan2 460 . . . 4
19 ltl4ev 25095 . . . 4
2011, 18, 19syl2anc 642 . . 3
211, 20mpd 14 . 2
2221ex 423 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 357   wa 358  wbox 25073  wdia 25074  wcirc 25075   wunt 25076 This theorem is referenced by:  untindd  25122  untim1d  25123  untim2d  25124 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
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