Theorem bj-vjust 37050

Description: Justification theorem for dfv2 3453 if it were the definition. See also vjust 3451. (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 2715	. . 3 ⊢ 𝑧 ∈ {𝑥 ∣ ⊤}
2		vextru 2715	. . 3 ⊢ 𝑧 ∈ {𝑦 ∣ ⊤}
3	1, 2	2th 264	. 2 ⊢ (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤})
4	3	eqriv 2727	1 ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}

Syntax hints:   = wceq 1540  ⊤wtru 1541   ∈ wcel 2109  {cab 2708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722

This theorem is referenced by: (None)