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Mirrors > Home > MPE Home > Th. List > 2euex | Structured version Visualization version Unicode version |
Description: Double quantification with existential uniqueness. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
2euex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eu5 2335 |
. 2
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2 | excom 1937 |
. . . 4
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3 | nfe1 1928 |
. . . . . 6
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4 | 3 | nfmo 2326 |
. . . . 5
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5 | 19.8a 1945 |
. . . . . . 7
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6 | 5 | moimi 2359 |
. . . . . 6
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7 | df-mo 2314 |
. . . . . 6
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8 | 6, 7 | sylib 201 |
. . . . 5
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9 | 4, 8 | eximd 1970 |
. . . 4
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10 | 2, 9 | syl5bi 225 |
. . 3
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11 | 10 | impcom 436 |
. 2
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12 | 1, 11 | sylbi 200 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-eu 2313 df-mo 2314 |
This theorem is referenced by: 2exeu 2388 |
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