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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 |
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Ref | Expression |
---|---|
intminss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intminss.1 |
. . 3
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2 | 1 | elrab 3207 |
. 2
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3 | intss1 4262 |
. 2
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4 | 2, 3 | sylbir 218 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-rab 2757 df-v 3058 df-in 3422 df-ss 3429 df-int 4248 |
This theorem is referenced by: onintss 5491 knatar 6272 cardonle 8416 coftr 8728 wuncss 9195 ist1-3 20413 sigagenss 29019 ldgenpisyslem1 29033 dynkin 29037 nodenselem5 30622 nobndlem6 30634 nobndlem8 30636 fneint 31052 igenmin 32341 pclclN 33500 dfrcl2 36310 |
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