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Mirrors > Home > ILE Home > Th. List > mosubopt | Unicode version |
Description: "At most one" remains true inside ordered pair quantification. (Contributed by NM, 28-Aug-2007.) |
Ref | Expression |
---|---|
mosubopt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1518 |
. . 3
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2 | nfe1 1473 |
. . . 4
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3 | 2 | nfmo 2023 |
. . 3
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4 | nfa1 1518 |
. . . . 5
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5 | nfe1 1473 |
. . . . . . 7
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6 | 5 | nfex 1614 |
. . . . . 6
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7 | 6 | nfmo 2023 |
. . . . 5
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8 | copsexg 4199 |
. . . . . . . 8
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9 | 8 | mobidv 2039 |
. . . . . . 7
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10 | 9 | biimpcd 158 |
. . . . . 6
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11 | 10 | sps 1514 |
. . . . 5
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12 | 4, 7, 11 | exlimd 1574 |
. . . 4
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13 | 12 | sps 1514 |
. . 3
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14 | 1, 3, 13 | exlimd 1574 |
. 2
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15 | moanimv 2078 |
. . 3
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16 | simpl 108 |
. . . . . 6
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17 | 16 | 2eximi 1578 |
. . . . 5
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18 | 17 | ancri 322 |
. . . 4
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19 | 18 | moimi 2068 |
. . 3
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20 | 15, 19 | sylbir 134 |
. 2
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21 | 14, 20 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-14 2128 ax-ext 2136 ax-sep 4078 ax-pow 4130 ax-pr 4164 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1740 df-eu 2006 df-mo 2007 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-v 2711 df-un 3102 df-in 3104 df-ss 3111 df-pw 3541 df-sn 3562 df-pr 3563 df-op 3565 |
This theorem is referenced by: mosubop 4645 funoprabg 5910 |
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