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Mirrors > Home > MPE Home > Th. List > euan | Structured version Visualization version Unicode version |
Description: Introduction of a conjunct into uniqueness quantifier. (Contributed by NM, 19-Feb-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) (Proof shortened by Wolf Lammen, 24-Dec-2018.) |
Ref | Expression |
---|---|
moanim.1 |
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Ref | Expression |
---|---|
euan |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2322 |
. . . 4
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2 | moanim.1 |
. . . . 5
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3 | simpl 459 |
. . . . 5
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4 | 2, 3 | exlimi 1994 |
. . . 4
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5 | 1, 4 | syl 17 |
. . 3
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6 | ibar 507 |
. . . . 5
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7 | 2, 6 | eubid 2316 |
. . . 4
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8 | 7 | biimprcd 229 |
. . 3
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9 | 5, 8 | jcai 539 |
. 2
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10 | 7 | biimpa 487 |
. 2
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11 | 9, 10 | impbii 191 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-12 1932 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1663 df-nf 1667 df-eu 2302 |
This theorem is referenced by: euanv 2362 2eu7 2387 2eu8 2388 |
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