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Mirrors > Home > ILE Home > Th. List > ov2gf | Unicode version |
Description: The value of an operation class abstraction. A version of ovmpt2g 5793 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 2631 |
. . 3
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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 2240 |
. . . . 5
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7 | ov2gf.5 |
. . . . . . . 8
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8 | nfmpt21 5729 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 7, 8 | nfcxfr 2226 |
. . . . . . 7
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10 | nfcv 2229 |
. . . . . . 7
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11 | 2, 9, 10 | nfov 5693 |
. . . . . 6
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12 | 11, 5 | nfeq 2237 |
. . . . 5
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13 | 6, 12 | nfim 1510 |
. . . 4
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14 | ov2gf.2 |
. . . . . 6
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15 | 14 | nfel1 2240 |
. . . . 5
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16 | nfmpt22 5730 |
. . . . . . . 8
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17 | 7, 16 | nfcxfr 2226 |
. . . . . . 7
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18 | 3, 17, 4 | nfov 5693 |
. . . . . 6
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19 | 18, 14 | nfeq 2237 |
. . . . 5
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20 | 15, 19 | nfim 1510 |
. . . 4
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21 | ov2gf.3 |
. . . . . 6
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22 | 21 | eleq1d 2157 |
. . . . 5
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23 | oveq1 5673 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 23, 21 | eqeq12d 2103 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 22, 24 | imbi12d 233 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | ov2gf.4 |
. . . . . 6
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27 | 26 | eleq1d 2157 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | oveq2 5674 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 28, 26 | eqeq12d 2103 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 27, 29 | imbi12d 233 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 7 | ovmpt4g 5781 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 31 | 3expia 1146 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | 2, 3, 4, 13, 20, 25, 30, 32 | vtocl2gaf 2687 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | 1, 33 | syl5 32 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | 34 | 3impia 1141 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 ax-setind 4366 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-fal 1296 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ne 2257 df-ral 2365 df-rex 2366 df-v 2622 df-sbc 2842 df-dif 3002 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-opab 3906 df-id 4129 df-xp 4458 df-rel 4459 df-cnv 4460 df-co 4461 df-dm 4462 df-iota 4993 df-fun 5030 df-fv 5036 df-ov 5669 df-oprab 5670 df-mpt2 5671 |
This theorem is referenced by: (None) |
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