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Mirrors > Home > MPE Home > Th. List > vjust | Structured version Visualization version GIF version |
Description: Justification theorem for df-v 3443. (Contributed by Rodolfo Medina, 27-Apr-2010.) |
Ref | Expression |
---|---|
vjust | ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑦 ∣ 𝑦 = 𝑦} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 2014 | . . . 4 ⊢ 𝑥 = 𝑥 | |
2 | 1 | vexw 2719 | . . 3 ⊢ 𝑧 ∈ {𝑥 ∣ 𝑥 = 𝑥} |
3 | equid 2014 | . . . 4 ⊢ 𝑦 = 𝑦 | |
4 | 3 | vexw 2719 | . . 3 ⊢ 𝑧 ∈ {𝑦 ∣ 𝑦 = 𝑦} |
5 | 2, 4 | 2th 263 | . 2 ⊢ (𝑧 ∈ {𝑥 ∣ 𝑥 = 𝑥} ↔ 𝑧 ∈ {𝑦 ∣ 𝑦 = 𝑦}) |
6 | 5 | eqriv 2733 | 1 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑦 ∣ 𝑦 = 𝑦} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1540 ∈ wcel 2105 {cab 2713 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-9 2115 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ex 1781 df-sb 2067 df-clab 2714 df-cleq 2728 |
This theorem is referenced by: (None) |
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