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Mirrors > Home > MPE Home > Th. List > Mathboxes > pwuniss | Structured version Visualization version Unicode version |
Description: Condition for a class union to be a subset. (Contributed by Thierry Arnoux, 21-Jun-2020.) |
Ref | Expression |
---|---|
pwuniss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniss 4458 | . 2 | |
2 | unipw 4918 | . 2 | |
3 | 1, 2 | syl6sseq 3651 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wss 3574 cpw 4158 cuni 4436 |
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 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 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-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-pw 4160 df-sn 4178 df-pr 4180 df-uni 4437 |
This theorem is referenced by: elpwunicl 29371 pwldsys 30220 |
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