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Mirrors > Home > NFE Home > Th. List > mo2icl | Unicode version |
Description: Theorem for inferring "at most one." (Contributed by NM, 17-Oct-1996.) |
Ref | Expression |
---|---|
mo2icl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq2 2362 |
. . . . . 6
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2 | 1 | imbi2d 307 |
. . . . 5
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3 | 2 | albidv 1625 |
. . . 4
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4 | 3 | imbi1d 308 |
. . 3
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5 | 19.8a 1756 |
. . . 4
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6 | nfv 1619 |
. . . . 5
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7 | 6 | mo2 2233 |
. . . 4
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8 | 5, 7 | sylibr 203 |
. . 3
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9 | 4, 8 | vtoclg 2915 |
. 2
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10 | vex 2863 |
. . . . . . 7
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11 | eleq1 2413 |
. . . . . . 7
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12 | 10, 11 | mpbii 202 |
. . . . . 6
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13 | 12 | imim2i 13 |
. . . . 5
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14 | 13 | con3rr3 128 |
. . . 4
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15 | 14 | alimdv 1621 |
. . 3
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16 | alnex 1543 |
. . . 4
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17 | exmo 2249 |
. . . . 5
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18 | 17 | ori 364 |
. . . 4
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19 | 16, 18 | sylbi 187 |
. . 3
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20 | 15, 19 | syl6 29 |
. 2
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21 | 9, 20 | pm2.61i 156 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-v 2862 |
This theorem is referenced by: (None) |
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