Theorem 1oelpr 8452

Description: 1_o is an element of {∅, 1_o}. (Contributed by Umit Teoman Dogan, 10-Jun-2026.)

Assertion

Ref	Expression
1oelpr	⊢ 1o ∈ {∅, 1o}

Proof of Theorem 1oelpr

Step	Hyp	Ref	Expression
1		1oex 8451	. 2 ⊢ 1o ∈ V
2	1	prid2 4725	1 ⊢ 1o ∈ {∅, 1o}

Syntax hints:   ∈ wcel 2145  ∅c0 4288  {cpr 4587  1_oc1o 8434

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737  ax-sep 5251  ax-pr 5395

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1566  df-fal 1576  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-dif 3910  df-un 3912  df-nul 4289  df-sn 4586  df-pr 4588  df-suc 6356  df-1o 8441

This theorem is referenced by:  oaomoencom  43906