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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vjust | Structured version Visualization version GIF version |
Description: Justification theorem for dfv2 3435 if it were the definition. See also vjust 3433. (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-vjust | ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vextru 2722 | . . 3 ⊢ 𝑧 ∈ {𝑥 ∣ ⊤} | |
2 | vextru 2722 | . . 3 ⊢ 𝑧 ∈ {𝑦 ∣ ⊤} | |
3 | 1, 2 | 2th 263 | . 2 ⊢ (𝑧 ∈ {𝑥 ∣ ⊤} ↔ 𝑧 ∈ {𝑦 ∣ ⊤}) |
4 | 3 | eqriv 2735 | 1 ⊢ {𝑥 ∣ ⊤} = {𝑦 ∣ ⊤} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 ⊤wtru 1540 ∈ wcel 2106 {cab 2715 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-9 2116 ax-ext 2709 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1542 df-ex 1783 df-sb 2068 df-clab 2716 df-cleq 2730 |
This theorem is referenced by: (None) |
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