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Mirrors > Home > MPE Home > Th. List > 2eu1 | Structured version Visualization version Unicode version |
Description: Double existential uniqueness. This theorem shows a condition under which a "naive" definition matches the correct one. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Wolf Lammen, 11-Nov-2019.) |
Ref | Expression |
---|---|
2eu1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2eu2ex 2386 |
. . . . 5
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2 | df-mo 2315 |
. . . . . . 7
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3 | 2 | albii 1702 |
. . . . . 6
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4 | euim 2363 |
. . . . . . 7
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5 | 4 | ex 440 |
. . . . . 6
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6 | 3, 5 | syl5bi 225 |
. . . . 5
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7 | 1, 6 | syl 17 |
. . . 4
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8 | 7 | pm2.43b 52 |
. . 3
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9 | 2euswap 2388 |
. . . 4
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10 | 8, 9 | syld 45 |
. . 3
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11 | 8, 10 | jcad 540 |
. 2
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12 | 2exeu 2389 |
. 2
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13 | 11, 12 | impbid1 208 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-eu 2314 df-mo 2315 |
This theorem is referenced by: 2eu2 2394 2eu3 2395 2eu5 2397 |
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