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Mirrors > Home > ILE Home > Th. List > funimacnv | Unicode version |
Description: The image of the preimage of a function. (Contributed by NM, 25-May-2004.) |
Ref | Expression |
---|---|
funimacnv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funcnvres2 5193 | . . . 4 | |
2 | 1 | rneqd 4763 | . . 3 |
3 | df-ima 4547 | . . 3 | |
4 | 2, 3 | syl6reqr 2189 | . 2 |
5 | df-rn 4545 | . . . 4 | |
6 | 5 | ineq2i 3269 | . . 3 |
7 | dmres 4835 | . . 3 | |
8 | dfdm4 4726 | . . 3 | |
9 | 6, 7, 8 | 3eqtr2ri 2165 | . 2 |
10 | 4, 9 | syl6eq 2186 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 cin 3065 ccnv 4533 cdm 4534 crn 4535 cres 4536 cima 4537 wfun 5112 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 df-fun 5120 |
This theorem is referenced by: funimass1 5195 funimass2 5196 |
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