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Mirrors > Home > MPE Home > Th. List > intss | Structured version Visualization version Unicode version |
Description: Intersection of subclasses. (Contributed by NM, 14-Oct-1999.) (Proof shortened by OpenAI, 25-Mar-2020.) |
Ref | Expression |
---|---|
intss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssralv 3666 | . . 3 | |
2 | 1 | ss2abdv 3675 | . 2 |
3 | dfint2 4477 | . 2 | |
4 | dfint2 4477 | . 2 | |
5 | 2, 3, 4 | 3sstr4g 3646 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 cab 2608 wral 2912 wss 3574 cint 4475 |
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-ral 2917 df-in 3581 df-ss 3588 df-int 4476 |
This theorem is referenced by: uniintsn 4514 intabs 4825 fiss 8330 tc2 8618 tcss 8620 tcel 8621 rankval4 8730 cfub 9071 cflm 9072 cflecard 9075 fin23lem26 9147 clsslem 13723 mrcss 16276 lspss 18984 lbsextlem3 19160 aspss 19332 clsss 20858 1stcfb 21248 ufinffr 21733 spanss 28207 ss2mcls 31465 pclssN 35180 dochspss 36667 clss2lem 37918 |
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