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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 36891 | . 2 ⊢ S = {〈𝑥, 𝑦〉 ∣ 𝑥 ⊆ 𝑦} | |
2 | 1 | relopabiv 5773 | 1 ⊢ Rel S |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3909 Rel wrel 5636 S cssr 36568 |
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 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2709 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2716 df-cleq 2730 df-clel 2816 df-v 3446 df-in 3916 df-ss 3926 df-opab 5167 df-xp 5637 df-rel 5638 df-ssr 36891 |
This theorem is referenced by: brssr 36894 issetssr 36896 brcnvssr 36899 extssr 36902 |
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