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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vjust | Structured version Visualization version GIF version |
Description: Justification theorem for dfv2 3481 if it were the definition. See also vjust 3479. (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-vjust | ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vextru 2719 | . . 3 ⊢ 𝑧 ∈ {𝑥 ∣ ⊤} | |
2 | vextru 2719 | . . 3 ⊢ 𝑧 ∈ {𝑦 ∣ ⊤} | |
3 | 1, 2 | 2th 264 | . 2 ⊢ (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤}) |
4 | 3 | eqriv 2732 | 1 ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ⊤wtru 1538 ∈ wcel 2106 {cab 2712 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1540 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 |
This theorem is referenced by: (None) |
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