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Theorem wrecseq3 8332
Description: Equality theorem for the well-ordered 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 2728 . 2 𝑅 = 𝑅
2 eqid 2728 . 2 𝐴 = 𝐴
3 wrecseq123 8326 . 2 ((𝑅 = 𝑅𝐴 = 𝐴𝐹 = 𝐺) → wrecs(𝑅, 𝐴, 𝐹) = wrecs(𝑅, 𝐴, 𝐺))
41, 2, 3mp3an12 1447 1 (𝐹 = 𝐺 → wrecs(𝑅, 𝐴, 𝐹) = wrecs(𝑅, 𝐴, 𝐺))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  wrecscwrecs 8323
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-ext 2699
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-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-ral 3059  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-uni 4913  df-br 5153  df-opab 5215  df-xp 5688  df-cnv 5690  df-co 5691  df-dm 5692  df-rn 5693  df-res 5694  df-ima 5695  df-pred 6310  df-iota 6505  df-fv 6561  df-ov 7429  df-frecs 8293  df-wrecs 8324
This theorem is referenced by:  recseq  8401  bpolylem  16032
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