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Mirrors > Home > MPE Home > Th. List > vjust | Structured version Visualization version GIF version |
Description: Justification theorem for df-v 3400. (Contributed by Rodolfo Medina, 27-Apr-2010.) |
Ref | Expression |
---|---|
vjust | ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑦 ∣ 𝑦 = 𝑦} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 2024 | . . . 4 ⊢ 𝑥 = 𝑥 | |
2 | 1 | vexw 2722 | . . 3 ⊢ 𝑧 ∈ {𝑥 ∣ 𝑥 = 𝑥} |
3 | equid 2024 | . . . 4 ⊢ 𝑦 = 𝑦 | |
4 | 3 | vexw 2722 | . . 3 ⊢ 𝑧 ∈ {𝑦 ∣ 𝑦 = 𝑦} |
5 | 2, 4 | 2th 267 | . 2 ⊢ (𝑧 ∈ {𝑥 ∣ 𝑥 = 𝑥} ↔ 𝑧 ∈ {𝑦 ∣ 𝑦 = 𝑦}) |
6 | 5 | eqriv 2735 | 1 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑦 ∣ 𝑦 = 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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