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Mirrors > Home > NFE 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 |
---|---|
moanim.1 |
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Ref | Expression |
---|---|
euan |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | moanim.1 |
. . . . . 6
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2 | simpl 443 |
. . . . . 6
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3 | 1, 2 | exlimi 1803 |
. . . . 5
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4 | 3 | adantr 451 |
. . . 4
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5 | simpr 447 |
. . . . . 6
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6 | 5 | eximi 1576 |
. . . . 5
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7 | 6 | adantr 451 |
. . . 4
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8 | nfe1 1732 |
. . . . . 6
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9 | 3 | a1d 22 |
. . . . . . . 8
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10 | 9 | ancrd 537 |
. . . . . . 7
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11 | 5, 10 | impbid2 195 |
. . . . . 6
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12 | 8, 11 | mobid 2238 |
. . . . 5
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13 | 12 | biimpa 470 |
. . . 4
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14 | 4, 7, 13 | jca32 521 |
. . 3
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15 | eu5 2242 |
. . 3
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16 | eu5 2242 |
. . . 4
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17 | 16 | anbi2i 675 |
. . 3
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18 | 14, 15, 17 | 3imtr4i 257 |
. 2
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19 | ibar 490 |
. . . 4
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20 | 1, 19 | eubid 2211 |
. . 3
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21 | 20 | biimpa 470 |
. 2
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22 | 18, 21 | impbii 180 |
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: euanv 2265 2eu7 2290 2eu8 2291 |
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