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Theorem wsuceq2 33798
Description: Equality theorem for well-founded successor. (Contributed by Scott Fenton, 13-Jun-2018.)
Assertion
Ref Expression
wsuceq2 (𝐴 = 𝐵 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐵, 𝑋))

Proof of Theorem wsuceq2
StepHypRef Expression
1 eqid 2740 . 2 𝑅 = 𝑅
2 eqid 2740 . 2 𝑋 = 𝑋
3 wsuceq123 33796 . 2 ((𝑅 = 𝑅𝐴 = 𝐵𝑋 = 𝑋) → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐵, 𝑋))
41, 2, 3mp3an13 1451 1 (𝐴 = 𝐵 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐵, 𝑋))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  wsuccwsuc 33792
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 2015  ax-8 2112  ax-9 2120  ax-ext 2711
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1545  df-fal 1555  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-ral 3071  df-rex 3072  df-rab 3075  df-v 3433  df-dif 3895  df-un 3897  df-in 3899  df-ss 3909  df-nul 4263  df-if 4466  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4846  df-br 5080  df-opab 5142  df-xp 5595  df-cnv 5597  df-dm 5599  df-rn 5600  df-res 5601  df-ima 5602  df-pred 6200  df-sup 9171  df-inf 9172  df-wsuc 33794
This theorem is referenced by: (None)
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