Theorem 0elpr01 11171

Description: 0 is an element of {0, 1}. (Contributed by Umit Teoman Dogan, 10-Jun-2026.)

Assertion

Ref	Expression
0elpr01	⊢ 0 ∈ {0, 1}

Proof of Theorem 0elpr01

Step	Hyp	Ref	Expression
1		c0ex 11170	. 2 ⊢ 0 ∈ V
2	1	prid1 4720	1 ⊢ 0 ∈ {0, 1}

Syntax hints:   ∈ wcel 2141  {cpr 4583  0cc0 11070  1c1 11071

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-1cn 11128  ax-icn 11129  ax-addcl 11130  ax-mulcl 11132  ax-i2m1 11138

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455  df-un 3909  df-sn 4582  df-pr 4584

This theorem is referenced by:  constrconj  34003