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Theorem tfr1ALT 27880
Description: tfr1 6958 via well-founded recursion. (Contributed by Scott Fenton, 22-Apr-2011.) (Revised by Mario Carneiro, 26-Jun-2015.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
tfrALT.1  |-  F  = recs ( G )
Assertion
Ref Expression
tfr1ALT  |-  F  Fn  On

Proof of Theorem tfr1ALT
StepHypRef Expression
1 epweon 6497 . 2  |-  _E  We  On
2 epse 4803 . 2  |-  _E Se  On
3 tfrALT.1 . . 3  |-  F  = recs ( G )
4 tfrALTlem 27879 . . 3  |- recs ( G )  = wrecs (  _E  ,  On ,  G
)
53, 4eqtri 2480 . 2  |-  F  = wrecs (  _E  ,  On ,  G )
61, 2, 5wfr1 27876 1  |-  F  Fn  On
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370    _E cep 4730   Oncon0 4819    Fn wfn 5513  recscrecs 6933  wrecscwrecs 27852
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-rep 4503  ax-sep 4513  ax-nul 4521  ax-pow 4570  ax-pr 4631  ax-un 6474
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 966  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-mo 2265  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-reu 2802  df-rmo 2803  df-rab 2804  df-v 3072  df-sbc 3287  df-csb 3389  df-dif 3431  df-un 3433  df-in 3435  df-ss 3442  df-pss 3444  df-nul 3738  df-if 3892  df-sn 3978  df-pr 3980  df-tp 3982  df-op 3984  df-uni 4192  df-iun 4273  df-br 4393  df-opab 4451  df-mpt 4452  df-tr 4486  df-eprel 4732  df-id 4736  df-po 4741  df-so 4742  df-fr 4779  df-se 4780  df-we 4781  df-ord 4822  df-on 4823  df-suc 4825  df-xp 4946  df-rel 4947  df-cnv 4948  df-co 4949  df-dm 4950  df-rn 4951  df-res 4952  df-ima 4953  df-iota 5481  df-fun 5520  df-fn 5521  df-f 5522  df-f1 5523  df-fo 5524  df-f1o 5525  df-fv 5526  df-recs 6934  df-pred 27761  df-wrecs 27853
This theorem is referenced by: (None)
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