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Theorem wsuceq3 33424
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 2738 . 2 𝑅 = 𝑅
2 eqid 2738 . 2 𝐴 = 𝐴
3 wsuceq123 33421 . 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 33417
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-3an 1090  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-ral 3058  df-rex 3059  df-rab 3062  df-v 3400  df-un 3848  df-in 3850  df-ss 3860  df-sn 4517  df-pr 4519  df-op 4523  df-uni 4797  df-br 5031  df-opab 5093  df-xp 5531  df-cnv 5533  df-dm 5535  df-rn 5536  df-res 5537  df-ima 5538  df-pred 6129  df-sup 8979  df-inf 8980  df-wsuc 33419
This theorem is referenced by: (None)
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