Theorem bj-vjust 37800

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 2745	. . 3 ⊢ 𝑧 ∈ {𝑥 ∣ ⊤}
2		vextru 2745	. . 3 ⊢ 𝑧 ∈ {𝑦 ∣ ⊤}
3	1, 2	2th 267	. 2 ⊢ (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤})
4	3	eqriv 2757	1 ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}

This proof depends on syntax axioms:   = wceq 1570  ⊤wtru 1571   ∈ wcel 2145  {cab 2738

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752

This theorem is used by: (None)