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Theorem wfrlem6 28925
 Description: Lemma for well-founded recursion. The definition generates a relationship. (Contributed by Scott Fenton, 8-Jun-2018.)
Hypothesis
Ref Expression
wfrlem6.1 wrecs
Assertion
Ref Expression
wfrlem6

Proof of Theorem wfrlem6
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 reluni 5123 . . 3
2 eqid 2467 . . . . 5
32wfrlem2 28921 . . . 4
4 funrel 5603 . . . 4
53, 4syl 16 . . 3
61, 5mprgbir 2828 . 2
7 wfrlem6.1 . . . 4 wrecs
8 df-wrecs 28913 . . . 4 wrecs
97, 8eqtri 2496 . . 3
109releqi 5084 . 2
116, 10mpbir 209 1
 Colors of variables: wff setvar class Syntax hints:   wa 369   w3a 973   wceq 1379  wex 1596   wcel 1767  cab 2452  wral 2814   wss 3476  cuni 4245   cres 5001   wrel 5004   wfun 5580   wfn 5581  cfv 5586  cpred 28820  wrecscwrecs 28912 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-iun 4327  df-br 4448  df-opab 4506  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-rn 5010  df-res 5011  df-ima 5012  df-iota 5549  df-fun 5588  df-fn 5589  df-fv 5594  df-pred 28821  df-wrecs 28913 This theorem is referenced by:  wfrlem11  28930
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