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Mirrors > Home > MPE Home > Th. List > un4 | Structured version Visualization version Unicode version |
Description: A rearrangement of the union of 4 classes. (Contributed by NM, 12-Aug-2004.) |
Ref | Expression |
---|---|
un4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | un12 3771 | . . 3 | |
2 | 1 | uneq2i 3764 | . 2 |
3 | unass 3770 | . 2 | |
4 | unass 3770 | . 2 | |
5 | 2, 3, 4 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cun 3572 |
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-un 3579 |
This theorem is referenced by: unundi 3774 unundir 3775 xpun 5176 resasplit 6074 ex-pw 27286 iunrelexp0 37994 |
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