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Mirrors > Home > NFE Home > Th. List > 2eu3 | Unicode version |
Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2eu3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfmo1 2215 |
. . . . 5
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2 | 1 | 19.31 1876 |
. . . 4
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3 | 2 | albii 1566 |
. . 3
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4 | nfmo1 2215 |
. . . . 5
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5 | 4 | nfal 1842 |
. . . 4
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6 | 5 | 19.32 1875 |
. . 3
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7 | 3, 6 | bitri 240 |
. 2
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8 | 2eu1 2284 |
. . . . . . 7
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9 | 8 | biimpd 198 |
. . . . . 6
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10 | ancom 437 |
. . . . . 6
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11 | 9, 10 | syl6ib 217 |
. . . . 5
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12 | 11 | adantld 453 |
. . . 4
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13 | 2eu1 2284 |
. . . . . 6
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14 | 13 | biimpd 198 |
. . . . 5
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15 | 14 | adantrd 454 |
. . . 4
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16 | 12, 15 | jaoi 368 |
. . 3
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17 | 2exeu 2281 |
. . . 4
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18 | 2exeu 2281 |
. . . . 5
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19 | 18 | ancoms 439 |
. . . 4
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20 | 17, 19 | jca 518 |
. . 3
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21 | 16, 20 | impbid1 194 |
. 2
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22 | 7, 21 | sylbi 187 |
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 |
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 |
This theorem is referenced by: (None) |
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