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Mirrors > Home > MPE Home > Th. List > xpun | Structured version Visualization version Unicode version |
Description: The Cartesian product of two unions. (Contributed by NM, 12-Aug-2004.) |
Ref | Expression |
---|---|
xpun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpundi 5171 | . 2 | |
2 | xpundir 5172 | . . 3 | |
3 | xpundir 5172 | . . 3 | |
4 | 2, 3 | uneq12i 3765 | . 2 |
5 | un4 3773 | . 2 | |
6 | 1, 4, 5 | 3eqtri 2648 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cun 3572 cxp 5112 |
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 df-opab 4713 df-xp 5120 |
This theorem is referenced by: ex-xp 27293 |
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