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Theorem wsuceq1 35320
Description: Equality theorem for well-founded successor. (Contributed by Scott Fenton, 13-Jun-2018.)
Assertion
Ref Expression
wsuceq1 (𝑅 = 𝑆 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑆, 𝐴, 𝑋))

Proof of Theorem wsuceq1
StepHypRef Expression
1 eqid 2726 . 2 𝐴 = 𝐴
2 eqid 2726 . 2 𝑋 = 𝑋
3 wsuceq123 35319 . 2 ((𝑅 = 𝑆𝐴 = 𝐴𝑋 = 𝑋) → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑆, 𝐴, 𝑋))
41, 2, 3mp3an23 1449 1 (𝑅 = 𝑆 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑆, 𝐴, 𝑋))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  wsuccwsuc 35315
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 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-ral 3056  df-rex 3065  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-opab 5204  df-xp 5675  df-cnv 5677  df-dm 5679  df-rn 5680  df-res 5681  df-ima 5682  df-pred 6293  df-sup 9436  df-inf 9437  df-wsuc 35317
This theorem is referenced by: (None)
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