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Mirrors > Home > MPE Home > Th. List > dfac5lem2 | Structured version Visualization version Unicode version |
Description: Lemma for dfac5 8564. (Contributed by NM, 12-Apr-2004.) |
Ref | Expression |
---|---|
dfac5lem.1 |
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Ref | Expression |
---|---|
dfac5lem2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfac5lem.1 |
. . . 4
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2 | 1 | unieqi 4210 |
. . 3
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3 | 2 | eleq2i 2523 |
. 2
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4 | eluniab 4212 |
. . 3
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5 | r19.42v 2947 |
. . . . 5
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6 | anass 655 |
. . . . 5
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7 | 5, 6 | bitr2i 254 |
. . . 4
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8 | 7 | exbii 1720 |
. . 3
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9 | rexcom4 3069 |
. . . 4
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10 | df-rex 2745 |
. . . 4
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11 | 9, 10 | bitr3i 255 |
. . 3
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12 | 4, 8, 11 | 3bitri 275 |
. 2
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13 | ancom 452 |
. . . . . . . . 9
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14 | ne0i 3739 |
. . . . . . . . . . 11
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15 | 14 | pm4.71i 638 |
. . . . . . . . . 10
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16 | 15 | anbi2i 701 |
. . . . . . . . 9
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17 | 13, 16 | bitr4i 256 |
. . . . . . . 8
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18 | 17 | exbii 1720 |
. . . . . . 7
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19 | snex 4644 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() | |
20 | vex 3050 |
. . . . . . . . 9
![]() ![]() ![]() ![]() | |
21 | 19, 20 | xpex 6600 |
. . . . . . . 8
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22 | eleq2 2520 |
. . . . . . . 8
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23 | 21, 22 | ceqsexv 3086 |
. . . . . . 7
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24 | 18, 23 | bitri 253 |
. . . . . 6
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25 | 24 | anbi2i 701 |
. . . . 5
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26 | opelxp 4867 |
. . . . . . 7
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27 | elsn 3984 |
. . . . . . . . 9
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28 | equcom 1864 |
. . . . . . . . 9
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29 | 27, 28 | bitri 253 |
. . . . . . . 8
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30 | 29 | anbi1i 702 |
. . . . . . 7
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31 | 26, 30 | bitri 253 |
. . . . . 6
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32 | 31 | anbi2i 701 |
. . . . 5
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33 | an12 807 |
. . . . 5
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34 | 25, 32, 33 | 3bitri 275 |
. . . 4
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35 | 34 | exbii 1720 |
. . 3
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36 | vex 3050 |
. . . 4
![]() ![]() ![]() ![]() | |
37 | elequ1 1896 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
38 | eleq2 2520 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
39 | 37, 38 | anbi12d 718 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
40 | 36, 39 | ceqsexv 3086 |
. . 3
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41 | 35, 40 | bitri 253 |
. 2
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42 | 3, 12, 41 | 3bitri 275 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-8 1891 ax-9 1898 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-sep 4528 ax-nul 4537 ax-pow 4584 ax-pr 4642 ax-un 6588 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 988 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-rab 2748 df-v 3049 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-nul 3734 df-if 3884 df-pw 3955 df-sn 3971 df-pr 3973 df-op 3977 df-uni 4202 df-opab 4465 df-xp 4843 df-rel 4844 |
This theorem is referenced by: dfac5lem5 8563 |
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