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Mirrors > Home > MPE Home > Th. List > intminss | Structured version Visualization version Unicode version |
Description: Under subset ordering, the intersection of a restricted class abstraction is less than or equal to any of its members. (Contributed by NM, 7-Sep-2013.) |
Ref | Expression |
---|---|
intminss.1 |
Ref | Expression |
---|---|
intminss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intminss.1 | . . 3 | |
2 | 1 | elrab 3363 | . 2 |
3 | intss1 4492 | . 2 | |
4 | 2, 3 | sylbir 225 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 crab 2916 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-rab 2921 df-v 3202 df-in 3581 df-ss 3588 df-int 4476 |
This theorem is referenced by: onintss 5775 knatar 6607 cardonle 8783 coftr 9095 wuncss 9567 ist1-3 21153 sigagenss 30212 ldgenpisyslem1 30226 dynkin 30230 fneint 32343 igenmin 33863 pclclN 35177 dfrcl2 37966 |
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