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Mirrors > Home > NFE Home > Th. List > frds | Unicode version |
Description: Substitution schema verson of frd 5923. (Contributed by SF, 19-Mar-2015.) |
Ref | Expression |
---|---|
frds.1 |
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frds.2 |
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frds.3 |
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frds.4 |
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frds.5 |
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Ref | Expression |
---|---|
frds |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frds.4 |
. . 3
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2 | dfrab2 3531 |
. . . . 5
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3 | df-rab 2624 |
. . . . 5
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4 | 2, 3 | eqtr3i 2375 |
. . . 4
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5 | frds.1 |
. . . . 5
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6 | brex 4690 |
. . . . . . 7
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7 | 1, 6 | syl 15 |
. . . . . 6
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8 | 7 | simprd 449 |
. . . . 5
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9 | inexg 4101 |
. . . . 5
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10 | 5, 8, 9 | sylancr 644 |
. . . 4
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11 | 4, 10 | syl5eqelr 2438 |
. . 3
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12 | ssab2 3351 |
. . . 4
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13 | 12 | a1i 10 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | frds.5 |
. . . . 5
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15 | df-rex 2621 |
. . . . 5
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16 | 14, 15 | sylib 188 |
. . . 4
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17 | abn0 3569 |
. . . 4
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18 | 16, 17 | sylibr 203 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 1, 11, 13, 18 | frd 5923 |
. 2
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20 | eleq1 2413 |
. . . . . 6
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21 | frds.2 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | 20, 21 | anbi12d 691 |
. . . . 5
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23 | 22 | rexab 3000 |
. . . 4
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24 | anass 630 |
. . . . 5
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25 | 24 | exbii 1582 |
. . . 4
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26 | 23, 25 | bitri 240 |
. . 3
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27 | impexp 433 |
. . . . . . 7
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28 | impexp 433 |
. . . . . . . 8
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29 | 28 | imbi2i 303 |
. . . . . . 7
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30 | 27, 29 | bitr4i 243 |
. . . . . 6
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31 | 30 | albii 1566 |
. . . . 5
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32 | eleq1 2413 |
. . . . . . 7
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33 | frds.3 |
. . . . . . 7
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34 | 32, 33 | anbi12d 691 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | 34 | ralab 2998 |
. . . . 5
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36 | df-ral 2620 |
. . . . 5
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37 | 31, 35, 36 | 3bitr4i 268 |
. . . 4
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38 | 37 | rexbii 2640 |
. . 3
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39 | df-rex 2621 |
. . 3
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40 | 26, 38, 39 | 3bitr4i 268 |
. 2
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41 | 19, 40 | sylib 188 |
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-13 1712 ax-14 1714 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4079 ax-xp 4080 ax-cnv 4081 ax-1c 4082 ax-sset 4083 ax-si 4084 ax-ins2 4085 ax-ins3 4086 ax-typlower 4087 ax-sn 4088 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3or 935 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ne 2519 df-ral 2620 df-rex 2621 df-reu 2622 df-rmo 2623 df-rab 2624 df-v 2862 df-sbc 3048 df-nin 3212 df-compl 3213 df-in 3214 df-un 3215 df-dif 3216 df-symdif 3217 df-ss 3260 df-pss 3262 df-nul 3552 df-if 3664 df-pw 3725 df-sn 3742 df-pr 3743 df-uni 3893 df-int 3928 df-opk 4059 df-1c 4137 df-pw1 4138 df-uni1 4139 df-xpk 4186 df-cnvk 4187 df-ins2k 4188 df-ins3k 4189 df-imak 4190 df-cok 4191 df-p6 4192 df-sik 4193 df-ssetk 4194 df-imagek 4195 df-idk 4196 df-iota 4340 df-0c 4378 df-addc 4379 df-nnc 4380 df-fin 4381 df-lefin 4441 df-ltfin 4442 df-ncfin 4443 df-tfin 4444 df-evenfin 4445 df-oddfin 4446 df-sfin 4447 df-spfin 4448 df-phi 4566 df-op 4567 df-proj1 4568 df-proj2 4569 df-opab 4624 df-br 4641 df-found 5906 |
This theorem is referenced by: weds 5939 |
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