Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wfrlem8 Unicode version

Theorem wfrlem8 25477
 Description: Lemma for well-founded recursion. Compute the prececessor class for an minimal element of . (Contributed by Scott Fenton, 21-Apr-2011.)
Hypotheses
Ref Expression
wfrlem6.1
wfrlem6.2
Assertion
Ref Expression
wfrlem8
Distinct variable groups:   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)   (,,)

Proof of Theorem wfrlem8
StepHypRef Expression
1 wfrlem6.1 . . . . 5
2 wfrlem6.2 . . . . 5
31, 2wfrlem7 25476 . . . 4
4 predpredss 25386 . . . 4
53, 4ax-mp 8 . . 3
65biantru 492 . 2
7 preddif 25405 . . . 4
87eqeq1i 2411 . . 3
9 ssdif0 3646 . . 3
108, 9bitr4i 244 . 2
11 eqss 3323 . 2
126, 10, 113bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   w3a 936  wex 1547   wceq 1649  cab 2390  wral 2666   cdif 3277   wss 3280  c0 3588  cuni 3975   cdm 4837   cres 4839   wfn 5408  cfv 5413  cpred 25381 This theorem is referenced by:  wfrlem10  25479 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-iun 4055  df-br 4173  df-opab 4227  df-xp 4843  df-rel 4844  df-cnv 4845  df-co 4846  df-dm 4847  df-rn 4848  df-res 4849  df-ima 4850  df-iota 5377  df-fun 5415  df-fn 5416  df-fv 5421  df-pred 25382
 Copyright terms: Public domain W3C validator