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Mirrors > Home > MPE Home > Th. List > Mathboxes > ssficl | Structured version Visualization version Unicode version |
Description: The class of all subsets of a class has the finite intersection property. (Contributed by Richard Penner, 1-Jan-2020.) (Proof shortened by Richard Penner, 3-Jan-2020.) |
Ref | Expression |
---|---|
ssficl.a |
Ref | Expression |
---|---|
ssficl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssficl.a | . 2 | |
2 | vex 3203 | . . 3 | |
3 | 2 | inex1 4799 | . 2 |
4 | sseq1 3626 | . 2 | |
5 | sseq1 3626 | . 2 | |
6 | sseq1 3626 | . 2 | |
7 | ssinss1 3841 | . . 3 | |
8 | 7 | adantr 481 | . 2 |
9 | 1, 3, 4, 5, 6, 8 | cllem0 37871 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wcel 1990 cab 2608 wral 2912 cvv 3200 cin 3573 wss 3574 |
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 ax-sep 4781 |
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-v 3202 df-in 3581 df-ss 3588 |
This theorem is referenced by: (None) |
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