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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-dtru | Structured version Visualization version Unicode version |
Description: Remove dependency on ax-13 2104 from dtru 4592. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-dtru |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-el 31477 |
. . . . 5
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2 | ax-nul 4527 |
. . . . . 6
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3 | sp 1957 |
. . . . . 6
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4 | 2, 3 | eximii 1717 |
. . . . 5
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5 | eeanv 2093 |
. . . . 5
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6 | 1, 4, 5 | mpbir2an 934 |
. . . 4
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7 | ax9 1917 |
. . . . . . 7
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8 | 7 | com12 31 |
. . . . . 6
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9 | 8 | con3dimp 448 |
. . . . 5
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10 | 9 | 2eximi 1716 |
. . . 4
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11 | 6, 10 | ax-mp 5 |
. . 3
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12 | equequ2 1876 |
. . . . . . 7
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13 | 12 | notbid 301 |
. . . . . 6
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14 | ax7 1868 |
. . . . . . . 8
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15 | 14 | con3d 140 |
. . . . . . 7
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16 | 15 | bj-spimevv 31389 |
. . . . . 6
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17 | 13, 16 | syl6bi 236 |
. . . . 5
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18 | ax7 1868 |
. . . . . . . 8
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19 | 18 | con3d 140 |
. . . . . . 7
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20 | 19 | bj-spimevv 31389 |
. . . . . 6
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21 | 20 | a1d 25 |
. . . . 5
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22 | 17, 21 | pm2.61i 169 |
. . . 4
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23 | 22 | exlimivv 1786 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 11, 23 | ax-mp 5 |
. 2
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25 | exnal 1707 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
26 | 24, 25 | mpbi 213 |
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-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-nul 4527 ax-pow 4579 |
This theorem depends on definitions: df-bi 190 df-an 378 df-tru 1455 df-ex 1672 df-nf 1676 |
This theorem is referenced by: bj-axc16b 31479 bj-eunex 31480 bj-dtrucor 31481 bj-dvdemo1 31483 |
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