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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-intss | Structured version Visualization version Unicode version |
Description: A nonempty intersection of a family of subsets of a class is included in that class. (Contributed by BJ, 7-Dec-2021.) |
Ref | Expression |
---|---|
bj-intss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sspwuni 4611 | . . 3 | |
2 | 1 | biimpi 206 | . 2 |
3 | intssuni 4499 | . 2 | |
4 | sstr 3611 | . . 3 | |
5 | 4 | expcom 451 | . 2 |
6 | 2, 3, 5 | syl2im 40 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wne 2794 wss 3574 c0 3915 cpw 4158 cuni 4436 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-ne 2795 df-ral 2917 df-rex 2918 df-v 3202 df-dif 3577 df-in 3581 df-ss 3588 df-nul 3916 df-pw 4160 df-uni 4437 df-int 4476 |
This theorem is referenced by: bj-0int 33055 |
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