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Mirrors > Home > ILE Home > Th. List > euan | Unicode version |
Description: Introduction of a conjunct into uniqueness quantifier. (Contributed by NM, 19-Feb-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
euan.1 |
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Ref | Expression |
---|---|
euan |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euan.1 |
. . . . . 6
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2 | simpl 102 |
. . . . . 6
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3 | 1, 2 | exlimih 1481 |
. . . . 5
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4 | 3 | adantr 261 |
. . . 4
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5 | simpr 103 |
. . . . . 6
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6 | 5 | eximi 1488 |
. . . . 5
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7 | 6 | adantr 261 |
. . . 4
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8 | hbe1 1381 |
. . . . . 6
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9 | 3 | a1d 22 |
. . . . . . . 8
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10 | 9 | ancrd 309 |
. . . . . . 7
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11 | 5, 10 | impbid2 131 |
. . . . . 6
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12 | 8, 11 | mobidh 1931 |
. . . . 5
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13 | 12 | biimpa 280 |
. . . 4
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14 | 4, 7, 13 | jca32 293 |
. . 3
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15 | eu5 1944 |
. . 3
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16 | eu5 1944 |
. . . 4
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17 | 16 | anbi2i 430 |
. . 3
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18 | 14, 15, 17 | 3imtr4i 190 |
. 2
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19 | ibar 285 |
. . . 4
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20 | 1, 19 | eubidh 1903 |
. . 3
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21 | 20 | biimpa 280 |
. 2
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22 | 18, 21 | impbii 117 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 |
This theorem is referenced by: euanv 1954 2eu7 1991 |
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