Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > funiunfvdm | Unicode version |
Description: The indexed union of a function's values is the union of its image under the index class. This theorem is a slight variation of fniunfv 5631. (Contributed by Jim Kingdon, 10-Jan-2019.) |
Ref | Expression |
---|---|
funiunfvdm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fniunfv 5631 | . 2 | |
2 | imadmrn 4861 | . . . 4 | |
3 | fndm 5192 | . . . . 5 | |
4 | 3 | imaeq2d 4851 | . . . 4 |
5 | 2, 4 | syl5eqr 2164 | . . 3 |
6 | 5 | unieqd 3717 | . 2 |
7 | 1, 6 | eqtrd 2150 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 cuni 3706 ciun 3783 cdm 4509 crn 4510 cima 4512 wfn 5088 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-iun 3785 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-fv 5101 |
This theorem is referenced by: funiunfvdmf 5633 eluniimadm 5634 |
Copyright terms: Public domain | W3C validator |