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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 38198 | . 2 ⊢ S = {〈𝑥, 𝑦〉 ∣ 𝑥 ⊆ 𝑦} | |
2 | 1 | relopabiv 5828 | 1 ⊢ Rel S |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3947 Rel wrel 5689 S cssr 37881 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2697 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1537 df-ex 1775 df-sb 2061 df-clab 2704 df-cleq 2718 df-clel 2803 df-v 3464 df-ss 3964 df-opab 5218 df-xp 5690 df-rel 5691 df-ssr 38198 |
This theorem is referenced by: brssr 38201 issetssr 38203 brcnvssr 38206 extssr 38209 |
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