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Theorem nfwrecs 7038
 Description: Bound-variable hypothesis builder for the well-founded recursive function generator. (Contributed by Scott Fenton, 9-Jun-2018.)
Hypotheses
Ref Expression
nfwrecs.1
nfwrecs.2
nfwrecs.3
Assertion
Ref Expression
nfwrecs wrecs

Proof of Theorem nfwrecs
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-wrecs 7036 . 2 wrecs
2 nfv 1754 . . . . . 6
3 nfcv 2591 . . . . . . . 8
4 nfwrecs.2 . . . . . . . 8
53, 4nfss 3463 . . . . . . 7
6 nfwrecs.1 . . . . . . . . . 10
7 nfcv 2591 . . . . . . . . . 10
86, 4, 7nfpred 5404 . . . . . . . . 9
98, 3nfss 3463 . . . . . . . 8
103, 9nfral 2818 . . . . . . 7
115, 10nfan 1986 . . . . . 6
12 nfwrecs.3 . . . . . . . . 9
13 nfcv 2591 . . . . . . . . . 10
1413, 8nfres 5127 . . . . . . . . 9
1512, 14nffv 5888 . . . . . . . 8
1615nfeq2 2608 . . . . . . 7
173, 16nfral 2818 . . . . . 6
182, 11, 17nf3an 1988 . . . . 5
1918nfex 2006 . . . 4
2019nfab 2595 . . 3
2120nfuni 4228 . 2
221, 21nfcxfr 2589 1 wrecs
 Colors of variables: wff setvar class Syntax hints:   wa 370   w3a 982   wceq 1437  wex 1659  cab 2414  wnfc 2577  wral 2782   wss 3442  cuni 4222   cres 4856  cpred 5398   wfn 5596  cfv 5601  wrecscwrecs 7035 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-uni 4223  df-br 4427  df-opab 4485  df-xp 4860  df-cnv 4862  df-dm 4864  df-rn 4865  df-res 4866  df-ima 4867  df-pred 5399  df-iota 5565  df-fv 5609  df-wrecs 7036 This theorem is referenced by:  nfrecs  7101
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