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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vjust | Structured version Visualization version GIF version | ||
| Description: Justification theorem for dfv2 3483 if it were the definition. See also vjust 3481. (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.) |
| Ref | Expression |
|---|---|
| bj-vjust | ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤} |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | vextru 2721 | . . 3 ⊢ 𝑧 ∈ {𝑥 ∣ ⊤} | |
| 2 | vextru 2721 | . . 3 ⊢ 𝑧 ∈ {𝑦 ∣ ⊤} | |
| 3 | 1, 2 | 2th 264 | . 2 ⊢ (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤}) |
| 4 | 3 | eqriv 2734 | 1 ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤} |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ⊤wtru 1541 ∈ 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-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 |
| This theorem is referenced by: (None) |
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