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Mirrors > Home > ILE Home > Th. List > moexexdc | Unicode version |
Description: "At most one" double quantification. (Contributed by Jim Kingdon, 5-Jul-2018.) |
Ref | Expression |
---|---|
moexexdc.1 |
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Ref | Expression |
---|---|
moexexdc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 836 |
. 2
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2 | hbmo1 2076 |
. . . . . 6
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3 | hba1 1551 |
. . . . . . 7
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4 | hbe1 1506 |
. . . . . . . 8
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5 | 4 | hbmo 2077 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 3, 5 | hbim 1556 |
. . . . . 6
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7 | 2, 6 | hbim 1556 |
. . . . 5
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8 | moexexdc.1 |
. . . . . . . 8
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9 | 8 | nfri 1530 |
. . . . . . 7
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10 | 9 | hbmo 2077 |
. . . . . . 7
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11 | mopick 2116 |
. . . . . . . . 9
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12 | 11 | ex 115 |
. . . . . . . 8
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13 | 12 | com3r 79 |
. . . . . . 7
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14 | 9, 10, 13 | alrimdh 1490 |
. . . . . 6
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15 | moim 2102 |
. . . . . . 7
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16 | 15 | spsd 1549 |
. . . . . 6
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17 | 14, 16 | syl6 33 |
. . . . 5
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18 | 7, 17 | exlimih 1604 |
. . . 4
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19 | 9 | hbex 1647 |
. . . . . . . . 9
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20 | exsimpl 1628 |
. . . . . . . . 9
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21 | 19, 20 | exlimih 1604 |
. . . . . . . 8
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22 | 21 | con3i 633 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | mon 2067 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 22, 23 | syl 14 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 24 | a1d 22 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 25 | a1d 22 |
. . . 4
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27 | 18, 26 | jaoi 717 |
. . 3
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28 | 27 | impd 254 |
. 2
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29 | 1, 28 | sylbi 121 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-dc 836 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 |
This theorem is referenced by: 2moswapdc 2128 |
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