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Theorem wfrrel 8350
Description: The well-ordered recursion generator generates a relation. Avoids the axiom of replacement. (Contributed by Scott Fenton, 8-Jun-2018.) (Proof shortened by Scott Fenton, 17-Nov-2024.)
Hypothesis
Ref Expression
wfrrel.1 𝐹 = wrecs(𝑅, 𝐴, 𝐺)
Assertion
Ref Expression
wfrrel Rel 𝐹

Proof of Theorem wfrrel
StepHypRef Expression
1 wfrrel.1 . . 3 𝐹 = wrecs(𝑅, 𝐴, 𝐺)
2 df-wrecs 8318 . . 3 wrecs(𝑅, 𝐴, 𝐺) = frecs(𝑅, 𝐴, (𝐺 ∘ 2nd ))
31, 2eqtri 2753 . 2 𝐹 = frecs(𝑅, 𝐴, (𝐺 ∘ 2nd ))
43frrrel 8312 1 Rel 𝐹
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  ccom 5682  Rel wrel 5683  2nd c2nd 7993  frecscfrecs 8286  wrecscwrecs 8317
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-nfc 2877  df-ral 3051  df-rex 3060  df-rab 3419  df-v 3463  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4323  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4910  df-iun 4999  df-br 5150  df-opab 5212  df-xp 5684  df-rel 5685  df-cnv 5686  df-co 5687  df-dm 5688  df-rn 5689  df-res 5690  df-ima 5691  df-pred 6307  df-iota 6501  df-fun 6551  df-fn 6552  df-fv 6557  df-ov 7422  df-frecs 8287  df-wrecs 8318
This theorem is referenced by: (None)
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