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Mirrors > Home > ILE 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 | nfa1 1434 |
. . . . 5
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2 | vex 2560 |
. . . . . . . 8
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3 | eleq1 2100 |
. . . . . . . 8
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4 | 2, 3 | mpbii 136 |
. . . . . . 7
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5 | 4 | imim2i 12 |
. . . . . 6
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6 | 5 | sps 1430 |
. . . . 5
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7 | 1, 6 | eximd 1503 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 19.9v 1751 |
. . . 4
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9 | 7, 8 | syl6ib 150 |
. . 3
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10 | eqeq2 2049 |
. . . . . . . 8
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11 | 10 | imbi2d 219 |
. . . . . . 7
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12 | 11 | albidv 1705 |
. . . . . 6
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13 | 12 | imbi1d 220 |
. . . . 5
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14 | nfv 1421 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
15 | 14 | mo2r 1952 |
. . . . . 6
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16 | 15 | 19.23bi 1483 |
. . . . 5
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17 | 13, 16 | vtoclg 2613 |
. . . 4
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18 | 17 | com12 27 |
. . 3
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19 | 9, 18 | syld 40 |
. 2
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20 | moabs 1949 |
. 2
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21 | 19, 20 | sylibr 137 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 |
This theorem is referenced by: invdisj 3759 |
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