Theorem bj-vjust 36847

Description: Justification theorem for dfv2 3475 if it were the definition. See also vjust 3473. (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 2713	. . 3 ⊢ 𝑧 ∈ {𝑥 ∣ ⊤}
2		vextru 2713	. . 3 ⊢ 𝑧 ∈ {𝑦 ∣ ⊤}
3	1, 2	2th 263	. 2 ⊢ (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤})
4	3	eqriv 2726	1 ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}

Syntax hints:   = wceq 1534  ⊤wtru 1535   ∈ wcel 2100  {cab 2706

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-9 2110  ax-ext 2700

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1537  df-ex 1775  df-sb 2062  df-clab 2707  df-cleq 2721

This theorem is referenced by: (None)