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Theorem bj-vjust2 32206
 Description: Justification theorem for bj-df-v 32207. See also vjust 3174 and bj-vjust 31974. (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-vjust2 {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}

Proof of Theorem bj-vjust2
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 df-clab 2597 . . 3 (𝑧 ∈ {𝑥 ∣ ⊤} ↔ [𝑧 / 𝑥]⊤)
2 bj-sbfvv 31953 . . . 4 ([𝑧 / 𝑦]⊤ ↔ ⊤)
3 df-clab 2597 . . . 4 (𝑧 ∈ {𝑦 ∣ ⊤} ↔ [𝑧 / 𝑦]⊤)
4 bj-sbfvv 31953 . . . 4 ([𝑧 / 𝑥]⊤ ↔ ⊤)
52, 3, 43bitr4ri 292 . . 3 ([𝑧 / 𝑥]⊤ ↔ 𝑧 ∈ {𝑦 ∣ ⊤})
61, 5bitri 263 . 2 (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤})
76eqriv 2607 1 {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ⊤wtru 1476  [wsb 1867   ∈ wcel 1977  {cab 2596 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-sb 1868  df-clab 2597  df-cleq 2603 This theorem is referenced by: (None)
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