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Theorem vjust 3399
Description: Justification theorem for df-v 3400. (Contributed by Rodolfo Medina, 27-Apr-2010.)
Assertion
Ref Expression
vjust {𝑥𝑥 = 𝑥} = {𝑦𝑦 = 𝑦}

Proof of Theorem vjust
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 equid 2024 . . . 4 𝑥 = 𝑥
21vexw 2722 . . 3 𝑧 ∈ {𝑥𝑥 = 𝑥}
3 equid 2024 . . . 4 𝑦 = 𝑦
43vexw 2722 . . 3 𝑧 ∈ {𝑦𝑦 = 𝑦}
52, 42th 267 . 2 (𝑧 ∈ {𝑥𝑥 = 𝑥} ↔ 𝑧 ∈ {𝑦𝑦 = 𝑦})
65eqriv 2735 1 {𝑥𝑥 = 𝑥} = {𝑦𝑦 = 𝑦}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  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-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730
This theorem is referenced by: (None)
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