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Mirrors > Home > NFE Home > Th. List > moexex | Unicode version |
Description: "At most one" double quantification. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
moexex.1 |
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Ref | Expression |
---|---|
moexex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfmo1 2215 |
. . . . 5
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2 | nfa1 1788 |
. . . . . 6
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3 | nfe1 1732 |
. . . . . . 7
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4 | 3 | nfmo 2221 |
. . . . . 6
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5 | 2, 4 | nfim 1813 |
. . . . 5
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6 | 1, 5 | nfim 1813 |
. . . 4
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7 | moexex.1 |
. . . . . 6
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8 | 7 | nfmo 2221 |
. . . . . 6
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9 | mopick 2266 |
. . . . . . . 8
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10 | 9 | ex 423 |
. . . . . . 7
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11 | 10 | com3r 73 |
. . . . . 6
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12 | 7, 8, 11 | alrimd 1769 |
. . . . 5
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13 | moim 2250 |
. . . . . 6
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14 | 13 | spsd 1755 |
. . . . 5
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15 | 12, 14 | syl6 29 |
. . . 4
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16 | 6, 15 | exlimi 1803 |
. . 3
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17 | 7 | nfex 1843 |
. . . . . . . 8
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18 | exsimpl 1592 |
. . . . . . . 8
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19 | 17, 18 | exlimi 1803 |
. . . . . . 7
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20 | 19 | con3i 127 |
. . . . . 6
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21 | exmo 2249 |
. . . . . . 7
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22 | 21 | ori 364 |
. . . . . 6
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23 | 20, 22 | syl 15 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 23 | a1d 22 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 24 | a1d 22 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 16, 25 | pm2.61i 156 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 26 | imp 418 |
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: moexexv 2274 2moswap 2279 |
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