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Theorem bj-vjust 36240
Description: Justification theorem for dfv2 3476 if it were the definition. See also vjust 3474. (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.
StepHypRef Expression
1 vextru 2715 . . 3 𝑧 ∈ {𝑥 ∣ ⊤}
2 vextru 2715 . . 3 𝑧 ∈ {𝑦 ∣ ⊤}
31, 22th 263 . 2 (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤})
43eqriv 2728 1 {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wtru 1541  wcel 2105  {cab 2708
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-9 2115  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723
This theorem is referenced by: (None)
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