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| Description: Justification theorem for df-v 3482. (Contributed by Rodolfo Medina, 27-Apr-2010.) | 
| Ref | Expression | 
|---|---|
| vjust | ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑦 ∣ 𝑦 = 𝑦} | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | equid 2011 | . . . 4 ⊢ 𝑥 = 𝑥 | |
| 2 | 1 | vexw 2720 | . . 3 ⊢ 𝑧 ∈ {𝑥 ∣ 𝑥 = 𝑥} | 
| 3 | equid 2011 | . . . 4 ⊢ 𝑦 = 𝑦 | |
| 4 | 3 | vexw 2720 | . . 3 ⊢ 𝑧 ∈ {𝑦 ∣ 𝑦 = 𝑦} | 
| 5 | 2, 4 | 2th 264 | . 2 ⊢ (𝑧 ∈ {𝑥 ∣ 𝑥 = 𝑥} ↔ 𝑧 ∈ {𝑦 ∣ 𝑦 = 𝑦}) | 
| 6 | 5 | eqriv 2734 | 1 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑦 ∣ 𝑦 = 𝑦} | 
| Colors of variables: wff setvar class | 
| Syntax hints: = wceq 1540 ∈ wcel 2108 {cab 2714 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-9 2118 ax-ext 2708 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 | 
| This theorem is referenced by: (None) | 
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