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Mirrors > Home > MPE Home > Th. List > f1mpt | Structured version Unicode version |
Description: Express injection for a mapping operation. (Contributed by Mario Carneiro, 2-Jan-2017.) |
Ref | Expression |
---|---|
f1mpt.1 |
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f1mpt.2 |
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Ref | Expression |
---|---|
f1mpt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1mpt.1 |
. . . 4
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2 | nfmpt1 4492 |
. . . 4
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3 | 1, 2 | nfcxfr 2614 |
. . 3
![]() ![]() ![]() ![]() |
4 | nfcv 2616 |
. . 3
![]() ![]() ![]() ![]() | |
5 | 3, 4 | dff13f 6085 |
. 2
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6 | 1 | fmpt 5976 |
. . 3
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7 | 6 | anbi1i 695 |
. 2
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8 | f1mpt.2 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 8 | eleq1d 2523 |
. . . . . 6
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10 | 9 | cbvralv 3053 |
. . . . 5
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11 | raaanv 3899 |
. . . . . 6
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12 | 1 | fvmpt2 5893 |
. . . . . . . . . . . . . 14
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13 | 8, 1 | fvmptg 5884 |
. . . . . . . . . . . . . 14
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14 | 12, 13 | eqeqan12d 2477 |
. . . . . . . . . . . . 13
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15 | 14 | an4s 822 |
. . . . . . . . . . . 12
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16 | 15 | imbi1d 317 |
. . . . . . . . . . 11
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17 | 16 | ex 434 |
. . . . . . . . . 10
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18 | 17 | ralimdva 2832 |
. . . . . . . . 9
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19 | ralbi 2959 |
. . . . . . . . 9
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20 | 18, 19 | syl6 33 |
. . . . . . . 8
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21 | 20 | ralimia 2817 |
. . . . . . 7
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22 | ralbi 2959 |
. . . . . . 7
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23 | 21, 22 | syl 16 |
. . . . . 6
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24 | 11, 23 | sylbir 213 |
. . . . 5
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25 | 10, 24 | sylan2b 475 |
. . . 4
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26 | 25 | anidms 645 |
. . 3
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27 | 26 | pm5.32i 637 |
. 2
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28 | 5, 7, 27 | 3bitr2i 273 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-sep 4524 ax-nul 4532 ax-pow 4581 ax-pr 4642 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-ral 2804 df-rex 2805 df-rab 2808 df-v 3080 df-sbc 3295 df-csb 3399 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-sn 3989 df-pr 3991 df-op 3995 df-uni 4203 df-br 4404 df-opab 4462 df-mpt 4463 df-id 4747 df-xp 4957 df-rel 4958 df-cnv 4959 df-co 4960 df-dm 4961 df-rn 4962 df-res 4963 df-ima 4964 df-iota 5492 df-fun 5531 df-fn 5532 df-f 5533 df-f1 5534 df-fv 5537 |
This theorem is referenced by: ismon2 14795 isepi2 14802 usgraidx2v 23483 |
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