Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dff3im | Unicode version |
Description: Property of a mapping. (Contributed by Jim Kingdon, 4-Jan-2019.) |
Ref | Expression |
---|---|
dff3im |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fssxp 5260 | . 2 | |
2 | ffun 5245 | . . . . . . . 8 | |
3 | 2 | adantr 274 | . . . . . . 7 |
4 | fdm 5248 | . . . . . . . . 9 | |
5 | 4 | eleq2d 2187 | . . . . . . . 8 |
6 | 5 | biimpar 295 | . . . . . . 7 |
7 | funfvop 5500 | . . . . . . 7 | |
8 | 3, 6, 7 | syl2anc 408 | . . . . . 6 |
9 | df-br 3900 | . . . . . 6 | |
10 | 8, 9 | sylibr 133 | . . . . 5 |
11 | funfvex 5406 | . . . . . . 7 | |
12 | breq2 3903 | . . . . . . . 8 | |
13 | 12 | spcegv 2748 | . . . . . . 7 |
14 | 11, 13 | syl 14 | . . . . . 6 |
15 | 3, 6, 14 | syl2anc 408 | . . . . 5 |
16 | 10, 15 | mpd 13 | . . . 4 |
17 | funmo 5108 | . . . . . 6 | |
18 | 2, 17 | syl 14 | . . . . 5 |
19 | 18 | adantr 274 | . . . 4 |
20 | eu5 2024 | . . . 4 | |
21 | 16, 19, 20 | sylanbrc 413 | . . 3 |
22 | 21 | ralrimiva 2482 | . 2 |
23 | 1, 22 | jca 304 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1453 wcel 1465 weu 1977 wmo 1978 wral 2393 cvv 2660 wss 3041 cop 3500 class class class wbr 3899 cxp 4507 cdm 4509 wfun 5087 wf 5089 cfv 5093 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-fv 5101 |
This theorem is referenced by: dff4im 5534 |
Copyright terms: Public domain | W3C validator |