Theorem 1oelpr 8441

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 8440	. 2 ⊢ 1o ∈ V
2	1	prid2 4721	1 ⊢ 1o ∈ {∅, 1o}

Syntax hints:   ∈ wcel 2141  ∅c0 4285  {cpr 4583  1_oc1o 8423

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733  ax-sep 5245  ax-pr 5389

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1562  df-fal 1572  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455  df-dif 3907  df-un 3909  df-nul 4286  df-sn 4582  df-pr 4584  df-suc 6346  df-1o 8430

This theorem is referenced by:  oaomoencom  43847