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Mirrors > Home > MPE Home > Th. List > mopick | Structured version Visualization version Unicode version |
Description: "At most one" picks a variable value, eliminating an existential quantifier. (Contributed by NM, 27-Jan-1997.) (Proof shortened by Wolf Lammen, 17-Sep-2019.) |
Ref | Expression |
---|---|
mopick |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mo2v 2477 | . . 3 | |
2 | sp 2053 | . . . . 5 | |
3 | pm3.45 879 | . . . . . . 7 | |
4 | 3 | aleximi 1759 | . . . . . 6 |
5 | sb56 2150 | . . . . . . 7 | |
6 | sp 2053 | . . . . . . 7 | |
7 | 5, 6 | sylbi 207 | . . . . . 6 |
8 | 4, 7 | syl6 35 | . . . . 5 |
9 | 2, 8 | syl5d 73 | . . . 4 |
10 | 9 | exlimiv 1858 | . . 3 |
11 | 1, 10 | sylbi 207 | . 2 |
12 | 11 | imp 445 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 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-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: eupick 2536 mopick2 2540 moexex 2541 morex 3390 imadif 5973 cmetss 23113 |
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