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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mo2v 2317 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | sp 1948 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | pm3.45 850 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | aleximi 1715 |
. . . . . 6
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5 | sb56 2092 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | sp 1948 |
. . . . . . 7
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7 | 5, 6 | sylbi 200 |
. . . . . 6
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8 | 4, 7 | syl6 34 |
. . . . 5
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9 | 2, 8 | syl5d 69 |
. . . 4
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10 | 9 | exlimiv 1787 |
. . 3
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11 | 1, 10 | sylbi 200 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 11 | imp 435 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-12 1944 |
This theorem depends on definitions: df-bi 190 df-an 377 df-ex 1675 df-nf 1679 df-eu 2314 df-mo 2315 |
This theorem is referenced by: eupick 2376 mopick2 2380 moexex 2381 morex 3234 imadif 5684 cmetss 22339 |
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