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Mirrors > Home > MPE Home > Th. List > intmin3 | Structured version Visualization version Unicode version |
Description: Under subset ordering, the intersection of a class abstraction is less than or equal to any of its members. (Contributed by NM, 3-Jul-2005.) |
Ref | Expression |
---|---|
intmin3.2 | |
intmin3.3 |
Ref | Expression |
---|---|
intmin3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intmin3.3 | . . 3 | |
2 | intmin3.2 | . . . 4 | |
3 | 2 | elabg 3351 | . . 3 |
4 | 1, 3 | mpbiri 248 | . 2 |
5 | intss1 4492 | . 2 | |
6 | 4, 5 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wcel 1990 cab 2608 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-v 3202 df-in 3581 df-ss 3588 df-int 4476 |
This theorem is referenced by: intabs 4825 intid 4926 |
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