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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 1489 |
. . . . 5
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2 | vex 2644 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
3 | eleq1 2162 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | mpbii 147 |
. . . . . . 7
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5 | 4 | imim2i 12 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 5 | sps 1485 |
. . . . 5
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7 | 1, 6 | eximd 1559 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 19.9v 1810 |
. . . 4
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9 | 7, 8 | syl6ib 160 |
. . 3
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10 | eqeq2 2109 |
. . . . . . . 8
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11 | 10 | imbi2d 229 |
. . . . . . 7
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12 | 11 | albidv 1763 |
. . . . . 6
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13 | 12 | imbi1d 230 |
. . . . 5
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14 | nfv 1476 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
15 | 14 | mo2r 2012 |
. . . . . 6
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16 | 15 | 19.23bi 1539 |
. . . . 5
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17 | 13, 16 | vtoclg 2701 |
. . . 4
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18 | 17 | com12 30 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 9, 18 | syld 45 |
. 2
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20 | moabs 2009 |
. 2
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21 | 19, 20 | sylibr 133 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-v 2643 |
This theorem is referenced by: invdisj 3869 |
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