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Theorem tfr1ALT 8347
Description: Alternate proof of tfr1 8344 using well-ordered 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 7710 . 2 E We On
2 epse 5617 . 2 E Se On
3 tfrALT.1 . . . 4 𝐹 = recs(𝐺)
4 df-recs 8318 . . . 4 recs(𝐺) = wrecs( E , On, 𝐺)
53, 4eqtri 2765 . . 3 𝐹 = wrecs( E , On, 𝐺)
65wfr1 8282 . 2 (( E We On ∧ E Se On) → 𝐹 Fn On)
71, 2, 6mp2an 691 1 𝐹 Fn On
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542   E cep 5537   Se wse 5587   We wwe 5588  Oncon0 6318   Fn wfn 6492  wrecscwrecs 8243  recscrecs 8317
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2708  ax-rep 5243  ax-sep 5257  ax-nul 5264  ax-pr 5385  ax-un 7673
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3or 1089  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2539  df-eu 2568  df-clab 2715  df-cleq 2729  df-clel 2815  df-nfc 2890  df-ne 2945  df-ral 3066  df-rex 3075  df-reu 3355  df-rab 3409  df-v 3448  df-sbc 3741  df-csb 3857  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-pss 3930  df-nul 4284  df-if 4488  df-pw 4563  df-sn 4588  df-pr 4590  df-op 4594  df-uni 4867  df-iun 4957  df-br 5107  df-opab 5169  df-mpt 5190  df-tr 5224  df-id 5532  df-eprel 5538  df-po 5546  df-so 5547  df-fr 5589  df-se 5590  df-we 5591  df-xp 5640  df-rel 5641  df-cnv 5642  df-co 5643  df-dm 5644  df-rn 5645  df-res 5646  df-ima 5647  df-pred 6254  df-ord 6321  df-on 6322  df-iota 6449  df-fun 6499  df-fn 6500  df-f 6501  df-f1 6502  df-fo 6503  df-f1o 6504  df-fv 6505  df-ov 7361  df-frecs 8213  df-wrecs 8244  df-recs 8318
This theorem is referenced by: (None)
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