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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dvelimf-o | Structured version Visualization version Unicode version |
Description: Proof of dvelimh 2181 that uses ax-c11 32504 but not ax-c15 32506, ax-c11n 32505, or ax-12 1944. Version of dvelimh 2181 using ax-c11 32504 instead of axc11 2159. (Contributed by NM, 12-Nov-2002.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dvelimf-o.1 |
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dvelimf-o.2 |
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dvelimf-o.3 |
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Ref | Expression |
---|---|
dvelimf-o |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1-o 32514 |
. . . . 5
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2 | ax-c11 32504 |
. . . . . 6
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3 | 2 | aecoms-o 32517 |
. . . . 5
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4 | 1, 3 | syl5 33 |
. . . 4
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5 | 4 | a1d 26 |
. . 3
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6 | hbnae-o 32544 |
. . . . . 6
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7 | hbnae-o 32544 |
. . . . . 6
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8 | 6, 7 | hban 2025 |
. . . . 5
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9 | hbnae-o 32544 |
. . . . . . 7
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10 | hbnae-o 32544 |
. . . . . . 7
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11 | 9, 10 | hban 2025 |
. . . . . 6
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12 | ax-c9 32507 |
. . . . . . 7
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13 | 12 | imp 435 |
. . . . . 6
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14 | dvelimf-o.1 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 14 | a1i 11 |
. . . . . 6
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16 | 11, 13, 15 | hbimd 2015 |
. . . . 5
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17 | 8, 16 | hbald 1937 |
. . . 4
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18 | 17 | ex 440 |
. . 3
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19 | 5, 18 | pm2.61i 169 |
. 2
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20 | dvelimf-o.2 |
. . 3
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21 | dvelimf-o.3 |
. . 3
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22 | 20, 21 | equsalh 2140 |
. 2
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23 | 22 | albii 1702 |
. 2
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24 | 19, 22, 23 | 3imtr3g 277 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-c5 32500 ax-c4 32501 ax-c7 32502 ax-c11 32504 ax-c9 32507 |
This theorem depends on definitions: df-bi 190 df-an 377 df-ex 1675 df-nf 1679 |
This theorem is referenced by: dveeq2-o 32549 dveeq1-o 32551 ax12el 32558 |
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