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Theorem wrecseq2 7961
 Description: Equality theorem for the well-founded recursive function generator. (Contributed by Scott Fenton, 7-Jun-2018.)
Assertion
Ref Expression
wrecseq2 (𝐴 = 𝐵 → wrecs(𝑅, 𝐴, 𝐹) = wrecs(𝑅, 𝐵, 𝐹))

Proof of Theorem wrecseq2
StepHypRef Expression
1 eqid 2758 . 2 𝑅 = 𝑅
2 eqid 2758 . 2 𝐹 = 𝐹
3 wrecseq123 7958 . 2 ((𝑅 = 𝑅𝐴 = 𝐵𝐹 = 𝐹) → wrecs(𝑅, 𝐴, 𝐹) = wrecs(𝑅, 𝐵, 𝐹))
41, 2, 3mp3an13 1449 1 (𝐴 = 𝐵 → wrecs(𝑅, 𝐴, 𝐹) = wrecs(𝑅, 𝐵, 𝐹))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538  wrecscwrecs 7956 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-ral 3075  df-rab 3079  df-v 3411  df-un 3863  df-in 3865  df-ss 3875  df-sn 4523  df-pr 4525  df-op 4529  df-uni 4799  df-br 5033  df-opab 5095  df-xp 5530  df-cnv 5532  df-dm 5534  df-rn 5535  df-res 5536  df-ima 5537  df-pred 6126  df-iota 6294  df-fv 6343  df-wrecs 7957 This theorem is referenced by:  csbrecsg  35025
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