Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > elpwincl1 | Structured version Visualization version Unicode version |
Description: Closure of intersection with regard to elementhood to a power set. (Contributed by Thierry Arnoux, 18-May-2020.) |
Ref | Expression |
---|---|
elpwincl.1 |
Ref | Expression |
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elpwincl1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpwincl.1 | . . 3 | |
2 | elpwi 4168 | . . 3 | |
3 | ssinss1 3841 | . . 3 | |
4 | 1, 2, 3 | 3syl 18 | . 2 |
5 | inex1g 4801 | . . 3 | |
6 | elpwg 4166 | . . 3 | |
7 | 1, 5, 6 | 3syl 18 | . 2 |
8 | 4, 7 | mpbird 247 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wcel 1990 cvv 3200 cin 3573 wss 3574 cpw 4158 |
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-v 3202 df-in 3581 df-ss 3588 df-pw 4160 |
This theorem is referenced by: difelcarsg 30372 inelcarsg 30373 carsgclctunlem1 30379 carsgclctunlem2 30381 carsgclctunlem3 30382 carsgclctun 30383 |
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