MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tfr1ALT Structured version   Unicode version

Theorem tfr1ALT 7103
Description: Alternate proof of tfr1 7100 using well-founded recursion. (Contributed by Scott Fenton, 3-Aug-2020.) (New usage is discouraged.) (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 6601 . 2  |-  _E  We  On
2 epse 4806 . 2  |-  _E Se  On
3 tfrALT.1 . . 3  |-  F  = recs ( G )
4 df-recs 7075 . . 3  |- recs ( G )  = wrecs (  _E  ,  On ,  G
)
53, 4eqtri 2431 . 2  |-  F  = wrecs (  _E  ,  On ,  G )
61, 2, 5wfr1 7039 1  |-  F  Fn  On
Colors of variables: wff setvar class
Syntax hints:    = wceq 1405    _E cep 4732   Oncon0 5410    Fn wfn 5564  wrecscwrecs 7012  recscrecs 7074
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-8 1844  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-rep 4507  ax-sep 4517  ax-nul 4525  ax-pow 4572  ax-pr 4630  ax-un 6574
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3or 975  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-reu 2761  df-rmo 2762  df-rab 2763  df-v 3061  df-sbc 3278  df-csb 3374  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-pss 3430  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-tp 3977  df-op 3979  df-uni 4192  df-iun 4273  df-br 4396  df-opab 4454  df-mpt 4455  df-tr 4490  df-eprel 4734  df-id 4738  df-po 4744  df-so 4745  df-fr 4782  df-se 4783  df-we 4784  df-xp 4829  df-rel 4830  df-cnv 4831  df-co 4832  df-dm 4833  df-rn 4834  df-res 4835  df-ima 4836  df-pred 5367  df-ord 5413  df-on 5414  df-iota 5533  df-fun 5571  df-fn 5572  df-f 5573  df-f1 5574  df-fo 5575  df-f1o 5576  df-fv 5577  df-wrecs 7013  df-recs 7075
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator