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Mirrors > Home > MPE Home > Th. List > moanim | Structured version Visualization version Unicode version |
Description: Introduction of a conjunct into "at most one" quantifier. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Wolf Lammen, 24-Dec-2018.) |
Ref | Expression |
---|---|
moanim.1 |
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Ref | Expression |
---|---|
moanim |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | moanim.1 |
. . . 4
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2 | ibar 507 |
. . . 4
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3 | 1, 2 | mobid 2318 |
. . 3
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4 | 3 | biimprcd 229 |
. 2
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5 | simpl 459 |
. . . . . 6
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6 | 1, 5 | exlimi 1995 |
. . . . 5
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7 | exmo 2324 |
. . . . . 6
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8 | 7 | ori 377 |
. . . . 5
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9 | 6, 8 | nsyl4 148 |
. . . 4
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10 | 9 | con1i 133 |
. . 3
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11 | moan 2353 |
. . 3
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12 | 10, 11 | ja 165 |
. 2
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13 | 4, 12 | 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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-12 1933 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-ex 1664 df-nf 1668 df-eu 2303 df-mo 2304 |
This theorem is referenced by: moanimv 2360 moanmo 2361 |
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