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Theorem wrecseq3 7562
Description: Equality theorem for the well-founded recursive function generator. (Contributed by Scott Fenton, 7-Jun-2018.)
Assertion
Ref Expression
wrecseq3 (𝐹 = 𝐺 → wrecs(𝑅, 𝐴, 𝐹) = wrecs(𝑅, 𝐴, 𝐺))

Proof of Theorem wrecseq3
StepHypRef Expression
1 eqid 2769 . 2 𝑅 = 𝑅
2 eqid 2769 . 2 𝐴 = 𝐴
3 wrecseq123 7558 . 2 ((𝑅 = 𝑅𝐴 = 𝐴𝐹 = 𝐺) → wrecs(𝑅, 𝐴, 𝐹) = wrecs(𝑅, 𝐴, 𝐺))
41, 2, 3mp3an12 1560 1 (𝐹 = 𝐺 → wrecs(𝑅, 𝐴, 𝐹) = wrecs(𝑅, 𝐴, 𝐺))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1629  wrecscwrecs 7556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1868  ax-4 1883  ax-5 1989  ax-6 2055  ax-7 2091  ax-9 2152  ax-10 2172  ax-11 2188  ax-12 2201  ax-13 2406  ax-ext 2749
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1071  df-tru 1632  df-ex 1851  df-nf 1856  df-sb 2048  df-clab 2756  df-cleq 2762  df-clel 2765  df-nfc 2900  df-ral 3064  df-rex 3065  df-rab 3068  df-v 3350  df-dif 3723  df-un 3725  df-in 3727  df-ss 3734  df-nul 4061  df-if 4223  df-sn 4314  df-pr 4316  df-op 4320  df-uni 4572  df-br 4784  df-opab 4844  df-xp 5254  df-cnv 5256  df-dm 5258  df-rn 5259  df-res 5260  df-ima 5261  df-pred 5822  df-iota 5993  df-fv 6038  df-wrecs 7557
This theorem is referenced by:  recseq  7621  bpolylem  14990
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