Theorem onuniorsuciOLD 7838

Description: Obsolete version of onuniorsuc 7835 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 = ∪ 𝐴 ∨ 𝐴 = suc ∪ 𝐴)

Proof of Theorem onuniorsuciOLD

Step	Hyp	Ref	Expression
1		onssi.1	. 2 ⊢ 𝐴 ∈ On
2		onuniorsuc 7835	. 2 ⊢ (𝐴 ∈ On → (𝐴 = ∪ 𝐴 ∨ 𝐴 = suc ∪ 𝐴))
3	1, 2	ax-mp 5	1 ⊢ (𝐴 = ∪ 𝐴 ∨ 𝐴 = suc ∪ 𝐴)

Syntax hints:   ∨ wo 845   = wceq 1533   ∈ wcel 2098  ∪ cuni 4904  Oncon0 6365  suc csuc 6367

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 2696  ax-sep 5295  ax-nul 5302  ax-pr 5424

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3or 1085  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-ne 2931  df-ral 3052  df-rex 3061  df-rab 3420  df-v 3465  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-pss 3961  df-nul 4320  df-if 4526  df-pw 4601  df-sn 4626  df-pr 4628  df-op 4632  df-uni 4905  df-br 5145  df-opab 5207  df-tr 5262  df-eprel 5577  df-po 5585  df-so 5586  df-fr 5628  df-we 5630  df-ord 6368  df-on 6369  df-suc 6371

This theorem is referenced by: (None)