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Mirrors > Home > ILE Home > Th. List > 2exeu | Unicode version |
Description: Double existential uniqueness implies double unique existential quantification. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2exeu |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1675 |
. . . . 5
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2 | hbe1 1506 |
. . . . . . . 8
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3 | 2 | hbmo 2077 |
. . . . . . 7
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4 | 3 | 19.41h 1696 |
. . . . . 6
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5 | 19.8a 1601 |
. . . . . . . . 9
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6 | 5 | moimi 2103 |
. . . . . . . 8
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7 | 6 | anim2i 342 |
. . . . . . 7
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8 | 7 | eximi 1611 |
. . . . . 6
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9 | 4, 8 | sylbir 135 |
. . . . 5
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10 | 1, 9 | sylanb 284 |
. . . 4
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11 | simpl 109 |
. . . . . 6
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12 | 11 | moimi 2103 |
. . . . 5
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13 | 12 | adantl 277 |
. . . 4
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14 | 10, 13 | anim12i 338 |
. . 3
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15 | 14 | ancoms 268 |
. 2
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16 | eu5 2085 |
. . 3
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17 | eu5 2085 |
. . 3
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18 | 16, 17 | anbi12i 460 |
. 2
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19 | eu5 2085 |
. . 3
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20 | eu5 2085 |
. . . . 5
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21 | 20 | exbii 1616 |
. . . 4
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22 | 20 | mobii 2075 |
. . . 4
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23 | 21, 22 | anbi12i 460 |
. . 3
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24 | 19, 23 | bitri 184 |
. 2
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25 | 15, 18, 24 | 3imtr4i 201 |
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-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-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 |
This theorem is referenced by: (None) |
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