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Mirrors > Home > MPE Home > Th. List > f1mpt | Structured version Visualization version Unicode version |
Description: Express injection for a mapping operation. (Contributed by Mario Carneiro, 2-Jan-2017.) |
Ref | Expression |
---|---|
f1mpt.1 | |
f1mpt.2 |
Ref | Expression |
---|---|
f1mpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1mpt.1 | . . . 4 | |
2 | nfmpt1 4747 | . . . 4 | |
3 | 1, 2 | nfcxfr 2762 | . . 3 |
4 | nfcv 2764 | . . 3 | |
5 | 3, 4 | dff13f 6513 | . 2 |
6 | 1 | fmpt 6381 | . . 3 |
7 | 6 | anbi1i 731 | . 2 |
8 | f1mpt.2 | . . . . . . 7 | |
9 | 8 | eleq1d 2686 | . . . . . 6 |
10 | 9 | cbvralv 3171 | . . . . 5 |
11 | raaanv 4083 | . . . . . 6 | |
12 | 1 | fvmpt2 6291 | . . . . . . . . . . . . . 14 |
13 | 8, 1 | fvmptg 6280 | . . . . . . . . . . . . . 14 |
14 | 12, 13 | eqeqan12d 2638 | . . . . . . . . . . . . 13 |
15 | 14 | an4s 869 | . . . . . . . . . . . 12 |
16 | 15 | imbi1d 331 | . . . . . . . . . . 11 |
17 | 16 | ex 450 | . . . . . . . . . 10 |
18 | 17 | ralimdva 2962 | . . . . . . . . 9 |
19 | ralbi 3068 | . . . . . . . . 9 | |
20 | 18, 19 | syl6 35 | . . . . . . . 8 |
21 | 20 | ralimia 2950 | . . . . . . 7 |
22 | ralbi 3068 | . . . . . . 7 | |
23 | 21, 22 | syl 17 | . . . . . 6 |
24 | 11, 23 | sylbir 225 | . . . . 5 |
25 | 10, 24 | sylan2b 492 | . . . 4 |
26 | 25 | anidms 677 | . . 3 |
27 | 26 | pm5.32i 669 | . 2 |
28 | 5, 7, 27 | 3bitr2i 288 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 cmpt 4729 wf 5884 wf1 5885 cfv 5888 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fv 5896 |
This theorem is referenced by: ismon2 16394 isepi2 16401 uspgredg2v 26116 usgredg2v 26119 aciunf1lem 29462 disjf1 39369 |
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