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Theorem wfrrel 7046
 Description: The well-founded recursion generator generates a relationship. (Contributed by Scott Fenton, 8-Jun-2018.)
Hypothesis
Ref Expression
wfrlem6.1 wrecs
Assertion
Ref Expression
wfrrel

Proof of Theorem wfrrel
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 reluni 4959 . . 3
2 eqid 2453 . . . . 5
32wfrlem2 7041 . . . 4
4 funrel 5602 . . . 4
53, 4syl 17 . . 3
61, 5mprgbir 2754 . 2
7 wfrlem6.1 . . . 4 wrecs
8 df-wrecs 7033 . . . 4 wrecs
97, 8eqtri 2475 . . 3
109releqi 4921 . 2
116, 10mpbir 213 1
 Colors of variables: wff setvar class Syntax hints:   wa 371   w3a 986   wceq 1446  wex 1665   wcel 1889  cab 2439  wral 2739   wss 3406  cuni 4201   cres 4839   wrel 4842  cpred 5382   wfun 5579   wfn 5580  cfv 5585  wrecscwrecs 7032 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 988  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ral 2744  df-rex 2745  df-rab 2748  df-v 3049  df-dif 3409  df-un 3411  df-in 3413  df-ss 3420  df-nul 3734  df-if 3884  df-sn 3971  df-pr 3973  df-op 3977  df-uni 4202  df-iun 4283  df-br 4406  df-opab 4465  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-pred 5383  df-iota 5549  df-fun 5587  df-fn 5588  df-fv 5593  df-wrecs 7033 This theorem is referenced by:  wfrfun  7051
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