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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.
StepHypRef Expression
1 vextru 2723 . . 3 𝑧 ∈ {𝑥 ∣ ⊤}
2 vextru 2723 . . 3 𝑧 ∈ {𝑦 ∣ ⊤}
31, 22th 267 . 2 (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤})
43eqriv 2735 1 {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}
Colors of variables: wff setvar class
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)
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