Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-vjust Structured version   Visualization version   GIF version

Theorem bj-vjust 37021
Description: Justification theorem for dfv2 3491 if it were the definition. See also vjust 3489. (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 2724 . . 3 𝑧 ∈ {𝑥 ∣ ⊤}
2 vextru 2724 . . 3 𝑧 ∈ {𝑦 ∣ ⊤}
31, 22th 264 . 2 (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤})
43eqriv 2737 1 {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  wtru 1538  wcel 2108  {cab 2717
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-9 2118  ax-ext 2711
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator