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Mirrors > Home > MPE Home > Th. List > reu3 | Structured version Visualization version Unicode version |
Description: A way to express restricted uniqueness. (Contributed by NM, 24-Oct-2006.) |
Ref | Expression |
---|---|
reu3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reurex 2995 |
. . 3
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2 | reu6 3215 |
. . . 4
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3 | biimp 198 |
. . . . . 6
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4 | 3 | ralimi 2796 |
. . . . 5
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5 | 4 | reximi 2852 |
. . . 4
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6 | 2, 5 | sylbi 200 |
. . 3
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7 | 1, 6 | jca 541 |
. 2
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8 | rexex 2843 |
. . . 4
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9 | 8 | anim2i 579 |
. . 3
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10 | eu3v 2347 |
. . . 4
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11 | df-reu 2763 |
. . . 4
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12 | df-rex 2762 |
. . . . 5
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13 | df-ral 2761 |
. . . . . . 7
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14 | impexp 453 |
. . . . . . . 8
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15 | 14 | albii 1699 |
. . . . . . 7
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16 | 13, 15 | bitr4i 260 |
. . . . . 6
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17 | 16 | exbii 1726 |
. . . . 5
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18 | 12, 17 | anbi12i 711 |
. . . 4
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19 | 10, 11, 18 | 3bitr4i 285 |
. . 3
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20 | 9, 19 | sylibr 217 |
. 2
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21 | 7, 20 | impbii 192 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-an 378 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-cleq 2464 df-clel 2467 df-ral 2761 df-rex 2762 df-reu 2763 df-rmo 2764 |
This theorem is referenced by: reu7 3221 2reu4a 38755 |
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