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Mirrors > Home > NFE Home > Th. List > 2eu2 | Unicode version |
Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2eu2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eumo 2244 |
. . 3
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2 | 2moex 2275 |
. . 3
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3 | 2eu1 2284 |
. . . 4
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4 | simpl 443 |
. . . 4
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5 | 3, 4 | syl6bi 219 |
. . 3
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6 | 1, 2, 5 | 3syl 18 |
. 2
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7 | 2exeu 2281 |
. . 3
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8 | 7 | expcom 424 |
. 2
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9 | 6, 8 | impbid 183 |
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: 2eu8 2291 |
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