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Theorem wsuceq3 34431
Description: Equality theorem for well-founded successor. (Contributed by Scott Fenton, 13-Jun-2018.)
Assertion
Ref Expression
wsuceq3 (𝑋 = 𝑌 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐴, 𝑌))

Proof of Theorem wsuceq3
StepHypRef Expression
1 eqid 2737 . 2 𝑅 = 𝑅
2 eqid 2737 . 2 𝐴 = 𝐴
3 wsuceq123 34428 . 2 ((𝑅 = 𝑅𝐴 = 𝐴𝑋 = 𝑌) → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐴, 𝑌))
41, 2, 3mp3an12 1452 1 (𝑋 = 𝑌 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐴, 𝑌))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  wsuccwsuc 34424
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-ral 3066  df-rex 3075  df-rab 3411  df-v 3450  df-dif 3918  df-un 3920  df-in 3922  df-ss 3932  df-nul 4288  df-if 4492  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4871  df-br 5111  df-opab 5173  df-xp 5644  df-cnv 5646  df-dm 5648  df-rn 5649  df-res 5650  df-ima 5651  df-pred 6258  df-sup 9385  df-inf 9386  df-wsuc 34426
This theorem is referenced by: (None)
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