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Mirrors > Home > MPE Home > Th. List > relin2 | Structured version Visualization version Unicode version |
Description: The intersection with a relation is a relation. (Contributed by NM, 17-Jan-2006.) |
Ref | Expression |
---|---|
relin2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss2 3834 | . 2 | |
2 | relss 5206 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 cin 3573 wss 3574 wrel 5119 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ss 3588 df-rel 5121 |
This theorem is referenced by: intasym 5511 asymref 5512 poirr2 5520 brdom3 9350 brdom5 9351 brdom4 9352 inxprnres 34060 relinxp 34069 clcnvlem 37930 |
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