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Theorem onuniorsuciOLD 7821
Description: Obsolete version of onuniorsuc 7818 as of 11-Jan-2025. (Contributed by NM, 13-Jun-1994.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
onssi.1 𝐴 ∈ On
Assertion
Ref Expression
onuniorsuciOLD (𝐴 = 𝐴𝐴 = suc 𝐴)

Proof of Theorem onuniorsuciOLD
StepHypRef Expression
1 onssi.1 . 2 𝐴 ∈ On
2 onuniorsuc 7818 . 2 (𝐴 ∈ On → (𝐴 = 𝐴𝐴 = suc 𝐴))
31, 2ax-mp 5 1 (𝐴 = 𝐴𝐴 = suc 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wo 844   = wceq 1533  wcel 2098   cuni 4899  Oncon0 6354  suc csuc 6356
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 2695  ax-sep 5289  ax-nul 5296  ax-pr 5417
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3or 1085  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ne 2933  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3943  df-un 3945  df-in 3947  df-ss 3957  df-pss 3959  df-nul 4315  df-if 4521  df-pw 4596  df-sn 4621  df-pr 4623  df-op 4627  df-uni 4900  df-br 5139  df-opab 5201  df-tr 5256  df-eprel 5570  df-po 5578  df-so 5579  df-fr 5621  df-we 5623  df-ord 6357  df-on 6358  df-suc 6360
This theorem is referenced by: (None)
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