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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 2343 |
. . . 4
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2 | moanim.1 |
. . . . 5
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3 | simpl 464 |
. . . . 5
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4 | 2, 3 | exlimi 2015 |
. . . 4
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5 | 1, 4 | syl 17 |
. . 3
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6 | ibar 512 |
. . . . 5
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7 | 2, 6 | eubid 2337 |
. . . 4
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8 | 7 | biimprcd 233 |
. . 3
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9 | 5, 8 | jcai 545 |
. 2
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10 | 7 | biimpa 492 |
. 2
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11 | 9, 10 | impbii 192 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-12 1950 |
This theorem depends on definitions: df-bi 190 df-an 378 df-ex 1672 df-nf 1676 df-eu 2323 |
This theorem is referenced by: euanv 2383 2eu7 2408 2eu8 2409 |
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