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Mirrors > Home > MPE Home > Th. List > Mathboxes > dffun10 | Structured version Visualization version Unicode version |
Description: Another potential definition of functionhood. Based on statements in http://people.math.gatech.edu/~belinfan/research/autoreas/otter/sum/fs/. (Contributed by Scott Fenton, 30-Aug-2017.) |
Ref | Expression |
---|---|
dffun10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrel 5207 | . . . 4 | |
2 | impexp 462 | . . . . . . 7 | |
3 | 2 | albii 1747 | . . . . . 6 |
4 | 19.21v 1868 | . . . . . 6 | |
5 | vex 3203 | . . . . . . . . . . 11 | |
6 | vex 3203 | . . . . . . . . . . 11 | |
7 | 5, 6 | opelco 5293 | . . . . . . . . . 10 |
8 | df-br 4654 | . . . . . . . . . . . 12 | |
9 | brv 4941 | . . . . . . . . . . . . . 14 | |
10 | brdif 4705 | . . . . . . . . . . . . . 14 | |
11 | 9, 10 | mpbiran 953 | . . . . . . . . . . . . 13 |
12 | 6 | ideq 5274 | . . . . . . . . . . . . . 14 |
13 | equcom 1945 | . . . . . . . . . . . . . 14 | |
14 | 12, 13 | bitri 264 | . . . . . . . . . . . . 13 |
15 | 11, 14 | xchbinx 324 | . . . . . . . . . . . 12 |
16 | 8, 15 | anbi12i 733 | . . . . . . . . . . 11 |
17 | 16 | exbii 1774 | . . . . . . . . . 10 |
18 | exanali 1786 | . . . . . . . . . 10 | |
19 | 7, 17, 18 | 3bitri 286 | . . . . . . . . 9 |
20 | 19 | con2bii 347 | . . . . . . . 8 |
21 | opex 4932 | . . . . . . . . 9 | |
22 | eldif 3584 | . . . . . . . . 9 | |
23 | 21, 22 | mpbiran 953 | . . . . . . . 8 |
24 | 20, 23 | bitr4i 267 | . . . . . . 7 |
25 | 24 | imbi2i 326 | . . . . . 6 |
26 | 3, 4, 25 | 3bitri 286 | . . . . 5 |
27 | 26 | 2albii 1748 | . . . 4 |
28 | 1, 27 | syl6rbbr 279 | . . 3 |
29 | 28 | pm5.32i 669 | . 2 |
30 | dffun4 5900 | . 2 | |
31 | sscoid 32020 | . 2 | |
32 | 29, 30, 31 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 wal 1481 wex 1704 wcel 1990 cvv 3200 cdif 3571 wss 3574 cop 4183 class class class wbr 4653 cid 5023 ccom 5118 wrel 5119 wfun 5882 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 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-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 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-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-fun 5890 |
This theorem is referenced by: (None) |
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