Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > dffun2 | Structured version Visualization version Unicode version |
Description: Alternate definition of a function. (Contributed by NM, 29-Dec-1996.) |
Ref | Expression |
---|---|
dffun2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fun 5890 | . 2 | |
2 | df-id 5024 | . . . . . 6 | |
3 | 2 | sseq2i 3630 | . . . . 5 |
4 | df-co 5123 | . . . . . 6 | |
5 | 4 | sseq1i 3629 | . . . . 5 |
6 | ssopab2b 5002 | . . . . 5 | |
7 | 3, 5, 6 | 3bitri 286 | . . . 4 |
8 | vex 3203 | . . . . . . . . . . . 12 | |
9 | vex 3203 | . . . . . . . . . . . 12 | |
10 | 8, 9 | brcnv 5305 | . . . . . . . . . . 11 |
11 | 10 | anbi1i 731 | . . . . . . . . . 10 |
12 | 11 | exbii 1774 | . . . . . . . . 9 |
13 | 12 | imbi1i 339 | . . . . . . . 8 |
14 | 19.23v 1902 | . . . . . . . 8 | |
15 | 13, 14 | bitr4i 267 | . . . . . . 7 |
16 | 15 | albii 1747 | . . . . . 6 |
17 | alcom 2037 | . . . . . 6 | |
18 | 16, 17 | bitri 264 | . . . . 5 |
19 | 18 | albii 1747 | . . . 4 |
20 | alcom 2037 | . . . 4 | |
21 | 7, 19, 20 | 3bitri 286 | . . 3 |
22 | 21 | anbi2i 730 | . 2 |
23 | 1, 22 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wex 1704 wss 3574 class class class wbr 4653 copab 4712 cid 5023 ccnv 5113 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-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-cnv 5122 df-co 5123 df-fun 5890 |
This theorem is referenced by: dffun3 5899 dffun4 5900 fundif 5935 fliftfun 6562 wfrlem5 7419 wfrfun 7425 fpwwe2lem11 9462 fclim 14284 invfun 16424 lmfun 21185 ulmdm 24147 fundmpss 31664 fununiq 31667 frrlem5 31784 frrlem5c 31786 fnsingle 32026 funimage 32035 funpartfun 32050 |
Copyright terms: Public domain | W3C validator |