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Mirrors > Home > NFE Home > Th. List > ov2gf | Unicode version |
Description: The value of an operation class abstraction. A version of ovmpt2g 5715 using bound-variable hypotheses. (Contributed by NM, 17-Aug-2006.) (Revised by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
ov2gf.a |
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ov2gf.c |
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ov2gf.d |
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ov2gf.1 |
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ov2gf.2 |
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ov2gf.3 |
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ov2gf.4 |
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ov2gf.5 |
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Ref | Expression |
---|---|
ov2gf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2867 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | ov2gf.a |
. . . 4
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3 | ov2gf.c |
. . . 4
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4 | ov2gf.d |
. . . 4
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5 | ov2gf.1 |
. . . . . 6
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6 | 5 | nfel1 2499 |
. . . . 5
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7 | ov2gf.5 |
. . . . . . . 8
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8 | nfmpt21 5673 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 7, 8 | nfcxfr 2486 |
. . . . . . 7
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10 | nfcv 2489 |
. . . . . . 7
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11 | 2, 9, 10 | nfov 5545 |
. . . . . 6
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12 | 11, 5 | nfeq 2496 |
. . . . 5
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13 | 6, 12 | nfim 1813 |
. . . 4
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14 | ov2gf.2 |
. . . . . 6
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15 | 14 | nfel1 2499 |
. . . . 5
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16 | nfmpt22 5674 |
. . . . . . . 8
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17 | 7, 16 | nfcxfr 2486 |
. . . . . . 7
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18 | 3, 17, 4 | nfov 5545 |
. . . . . 6
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19 | 18, 14 | nfeq 2496 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 15, 19 | nfim 1813 |
. . . 4
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21 | ov2gf.3 |
. . . . . 6
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22 | 21 | eleq1d 2419 |
. . . . 5
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23 | oveq1 5530 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 23, 21 | eqeq12d 2367 |
. . . . 5
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25 | 22, 24 | imbi12d 311 |
. . . 4
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26 | ov2gf.4 |
. . . . . 6
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27 | 26 | eleq1d 2419 |
. . . . 5
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28 | oveq2 5531 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 28, 26 | eqeq12d 2367 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 27, 29 | imbi12d 311 |
. . . 4
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31 | 7 | ovmpt4g 5710 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 31 | 3expia 1153 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | 2, 3, 4, 13, 20, 25, 30, 32 | vtocl2gaf 2921 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | 1, 33 | syl5 28 |
. 2
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35 | 34 | 3impia 1148 |
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-ima 4727 df-id 4767 df-cnv 4785 df-rn 4786 df-dm 4787 df-fun 4789 df-fv 4795 df-ov 5526 df-oprab 5528 df-mpt2 5654 |
This theorem is referenced by: (None) |
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