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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dvhopclN | Structured version Visualization version GIF version |
Description: Closure of a DVecH vector expressed as ordered pair. (Contributed by NM, 20-Nov-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dvhopclN | ⊢ ((𝐹 ∈ 𝑇 ∧ 𝑈 ∈ 𝐸) → 〈𝐹, 𝑈〉 ∈ (𝑇 × 𝐸)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxpi 5725 | 1 ⊢ ((𝐹 ∈ 𝑇 ∧ 𝑈 ∈ 𝐸) → 〈𝐹, 𝑈〉 ∈ (𝑇 × 𝐸)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∈ wcel 2105 〈cop 4636 × cxp 5686 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 ax-sep 5301 ax-nul 5311 ax-pr 5437 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1539 df-fal 1549 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-ral 3059 df-rex 3068 df-rab 3433 df-v 3479 df-dif 3965 df-un 3967 df-ss 3979 df-nul 4339 df-if 4531 df-sn 4631 df-pr 4633 df-op 4637 df-opab 5210 df-xp 5694 |
This theorem is referenced by: (None) |
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