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Mirrors > Home > MPE Home > Th. List > 2mo2 | Structured version Visualization version Unicode version |
Description: This theorem extends the idea of "at most one" to expressions in two set variables ("at most one pair and ". Note: this is not expressed by ). 2eu4 2556 relates this extension to double existential uniqueness, if at least one pair exists. (Contributed by Wolf Lammen, 26-Oct-2019.) |
Ref | Expression |
---|---|
2mo2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eeanv 2182 | . 2 | |
2 | jcab 907 | . . . . 5 | |
3 | 2 | 2albii 1748 | . . . 4 |
4 | 19.26-2 1799 | . . . 4 | |
5 | 19.23v 1902 | . . . . . 6 | |
6 | 5 | albii 1747 | . . . . 5 |
7 | alcom 2037 | . . . . . 6 | |
8 | 19.23v 1902 | . . . . . . 7 | |
9 | 8 | albii 1747 | . . . . . 6 |
10 | 7, 9 | bitri 264 | . . . . 5 |
11 | 6, 10 | anbi12i 733 | . . . 4 |
12 | 3, 4, 11 | 3bitri 286 | . . 3 |
13 | 12 | 2exbii 1775 | . 2 |
14 | mo2v 2477 | . . 3 | |
15 | mo2v 2477 | . . 3 | |
16 | 14, 15 | anbi12i 733 | . 2 |
17 | 1, 13, 16 | 3bitr4ri 293 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wex 1704 wmo 2471 |
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-10 2019 ax-11 2034 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-eu 2474 df-mo 2475 |
This theorem is referenced by: 2mo 2551 2eu4 2556 |
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