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Mirrors > Home > NFE Home > Th. List > fnfullfunlem1 | Unicode version |
Description: Lemma for fnfullfun 5858. Binary relationship over part one of the full function definition. (Contributed by SF, 9-Mar-2015.) |
Ref | Expression |
---|---|
fnfullfunlem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brex 4689 |
. . 3
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2 | 1 | simprd 449 |
. 2
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3 | brex 4689 |
. . . 4
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4 | 3 | simprd 449 |
. . 3
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5 | 4 | adantr 451 |
. 2
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6 | breq2 4643 |
. . . 4
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7 | breq2 4643 |
. . . . 5
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8 | eqeq2 2362 |
. . . . . . 7
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9 | 8 | imbi2d 307 |
. . . . . 6
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10 | 9 | albidv 1625 |
. . . . 5
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11 | 7, 10 | anbi12d 691 |
. . . 4
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12 | 6, 11 | bibi12d 312 |
. . 3
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13 | brdif 4694 |
. . . 4
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14 | coi2 5095 |
. . . . . 6
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15 | 14 | breqi 4645 |
. . . . 5
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16 | brco 4883 |
. . . . . . 7
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17 | df-br 4640 |
. . . . . . . . . 10
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18 | vex 2862 |
. . . . . . . . . . . . 13
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19 | vex 2862 |
. . . . . . . . . . . . 13
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20 | 18, 19 | opex 4588 |
. . . . . . . . . . . 12
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21 | 20 | elcompl 3225 |
. . . . . . . . . . 11
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22 | df-br 4640 |
. . . . . . . . . . . 12
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23 | 19 | ideq 4870 |
. . . . . . . . . . . 12
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24 | 22, 23 | bitr3i 242 |
. . . . . . . . . . 11
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25 | 21, 24 | xchbinx 301 |
. . . . . . . . . 10
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26 | 17, 25 | bitri 240 |
. . . . . . . . 9
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27 | 26 | anbi2i 675 |
. . . . . . . 8
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28 | 27 | exbii 1582 |
. . . . . . 7
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29 | exanali 1585 |
. . . . . . 7
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30 | 16, 28, 29 | 3bitrri 263 |
. . . . . 6
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31 | 30 | con1bii 321 |
. . . . 5
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32 | 15, 31 | anbi12i 678 |
. . . 4
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33 | 13, 32 | bitri 240 |
. . 3
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34 | 12, 33 | vtoclg 2914 |
. 2
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35 | 2, 5, 34 | pm5.21nii 342 |
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 4078 ax-xp 4079 ax-cnv 4080 ax-1c 4081 ax-sset 4082 ax-si 4083 ax-ins2 4084 ax-ins3 4085 ax-typlower 4086 ax-sn 4087 |
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 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-reu 2621 df-rmo 2622 df-rab 2623 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-symdif 3216 df-ss 3259 df-pss 3261 df-nul 3551 df-if 3663 df-pw 3724 df-sn 3741 df-pr 3742 df-uni 3892 df-int 3927 df-opk 4058 df-1c 4136 df-pw1 4137 df-uni1 4138 df-xpk 4185 df-cnvk 4186 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-cok 4190 df-p6 4191 df-sik 4192 df-ssetk 4193 df-imagek 4194 df-idk 4195 df-iota 4339 df-0c 4377 df-addc 4378 df-nnc 4379 df-fin 4380 df-lefin 4440 df-ltfin 4441 df-ncfin 4442 df-tfin 4443 df-evenfin 4444 df-oddfin 4445 df-sfin 4446 df-spfin 4447 df-phi 4565 df-op 4566 df-proj1 4567 df-proj2 4568 df-opab 4623 df-br 4640 df-co 4726 df-id 4767 df-cnv 4785 |
This theorem is referenced by: fnfullfunlem2 5857 fvfullfunlem1 5861 fvfullfunlem2 5862 |
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