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Mirrors > Home > MPE Home > Th. List > mo2v | Structured version Visualization version Unicode version |
Description: Alternate definition of "at most one." Unlike mo2 2308, which is slightly more general, it does not depend on ax-11 1920 and ax-13 2091, whence it is preferable within predicate logic. Elsewhere, most theorems depend on these axioms anyway, so this advantage is no longer important. (Contributed by Wolf Lammen, 27-May-2019.) (Proof shortened by Wolf Lammen, 10-Nov-2019.) |
Ref | Expression |
---|---|
mo2v |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mo 2304 |
. 2
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2 | df-eu 2303 |
. . 3
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3 | 2 | imbi2i 314 |
. 2
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4 | alnex 1665 |
. . . . . . 7
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5 | pm2.21 112 |
. . . . . . . 8
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6 | 5 | alimi 1684 |
. . . . . . 7
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7 | 4, 6 | sylbir 217 |
. . . . . 6
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8 | 7 | eximi 1707 |
. . . . 5
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9 | 8 | 19.23bi 1949 |
. . . 4
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10 | biimp 197 |
. . . . . 6
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11 | 10 | alimi 1684 |
. . . . 5
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12 | 11 | eximi 1707 |
. . . 4
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13 | 9, 12 | ja 165 |
. . 3
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14 | nfia1 2037 |
. . . . . 6
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15 | id 22 |
. . . . . . . . . 10
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16 | ax12v 1934 |
. . . . . . . . . . 11
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17 | 16 | com12 32 |
. . . . . . . . . 10
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18 | 15, 17 | embantd 56 |
. . . . . . . . 9
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19 | 18 | spsd 1945 |
. . . . . . . 8
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20 | 19 | ancld 556 |
. . . . . . 7
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21 | albiim 1752 |
. . . . . . 7
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22 | 20, 21 | syl6ibr 231 |
. . . . . 6
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23 | 14, 22 | exlimi 1995 |
. . . . 5
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24 | 23 | eximdv 1764 |
. . . 4
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25 | 24 | com12 32 |
. . 3
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26 | 13, 25 | impbii 191 |
. 2
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27 | 1, 3, 26 | 3bitri 275 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-12 1933 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1664 df-nf 1668 df-eu 2303 df-mo 2304 |
This theorem is referenced by: mo2 2308 eu3v 2327 mo3 2336 sbmo 2344 moim 2348 mopick 2364 2mo2 2379 mo2icl 3217 moabex 4659 dffun3 5593 dffun6f 5596 grothprim 9259 bj-mo3OLD 31447 wl-mo2df 31899 wl-mo2t 31904 wl-mo3t 31905 dffrege115 36574 |
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