Theorem bj-vjust 34869

Description: Justification theorem for dfv2 3401 if it were the definition. See also vjust 3399. (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-vjust	⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}

Proof of Theorem bj-vjust

Dummy variable 𝑧 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		vextru 2723	. . 3 ⊢ 𝑧 ∈ {𝑥 ∣ ⊤}
2		vextru 2723	. . 3 ⊢ 𝑧 ∈ {𝑦 ∣ ⊤}
3	1, 2	2th 267	. 2 ⊢ (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤})
4	3	eqriv 2735	1 ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}

Syntax hints:   = wceq 1542  ⊤wtru 1543   ∈ wcel 2114  {cab 2716

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-9 2124  ax-ext 2710

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730

This theorem is referenced by: (None)