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Mathbox for Peter Mazsa |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > relssr | Structured version Visualization version GIF version |
Description: The subset relation is a relation. (Contributed by Peter Mazsa, 1-Aug-2019.) |
Ref | Expression |
---|---|
relssr | ⊢ Rel S |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ssr 38480 | . 2 ⊢ S = {〈𝑥, 𝑦〉 ∣ 𝑥 ⊆ 𝑦} | |
2 | 1 | relopabiv 5833 | 1 ⊢ Rel S |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3963 Rel wrel 5694 S cssr 38165 |
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-8 2108 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 df-clel 2814 df-v 3480 df-ss 3980 df-opab 5211 df-xp 5695 df-rel 5696 df-ssr 38480 |
This theorem is referenced by: brssr 38483 issetssr 38485 brcnvssr 38488 extssr 38491 |
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