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Mirrors > Home > MPE Home > Th. List > 2exeu | Structured version Visualization version Unicode version |
Description: Double existential uniqueness implies double uniqueness quantification. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Mario Carneiro, 22-Dec-2016.) |
Ref | Expression |
---|---|
2exeu |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eumo 2328 |
. . . 4
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2 | euex 2323 |
. . . . 5
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3 | 2 | moimi 2349 |
. . . 4
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4 | 1, 3 | syl 17 |
. . 3
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5 | 2euex 2373 |
. . 3
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6 | 4, 5 | anim12ci 571 |
. 2
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7 | eu5 2325 |
. 2
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8 | 6, 7 | sylibr 216 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-eu 2303 df-mo 2304 |
This theorem is referenced by: 2eu1 2382 2eu2 2383 2eu3 2384 |
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