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Mirrors > Home > MPE Home > Th. List > relrpss | Structured version Visualization version GIF version |
Description: The proper subset relation is a relation. (Contributed by Stefan O'Rear, 2-Nov-2014.) |
Ref | Expression |
---|---|
relrpss | ⊢ Rel [⊊] |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rpss 7084 | . 2 ⊢ [⊊] = {〈𝑥, 𝑦〉 ∣ 𝑥 ⊊ 𝑦} | |
2 | 1 | relopabi 5384 | 1 ⊢ Rel [⊊] |
Colors of variables: wff setvar class |
Syntax hints: ⊊ wpss 3724 Rel wrel 5254 [⊊] crpss 7083 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-9 2154 ax-10 2174 ax-11 2190 ax-12 2203 ax-13 2408 ax-ext 2751 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 835 df-3an 1073 df-tru 1634 df-ex 1853 df-nf 1858 df-sb 2050 df-clab 2758 df-cleq 2764 df-clel 2767 df-nfc 2902 df-rab 3070 df-v 3353 df-dif 3726 df-un 3728 df-in 3730 df-ss 3737 df-nul 4064 df-if 4226 df-sn 4317 df-pr 4319 df-op 4323 df-opab 4847 df-xp 5255 df-rel 5256 df-rpss 7084 |
This theorem is referenced by: brrpssg 7086 compssiso 9398 |
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