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Mirrors > Home > ILE Home > Th. List > f1ores | Unicode version |
Description: The restriction of a one-to-one function maps one-to-one onto the image. (Contributed by NM, 25-Mar-1998.) |
Ref | Expression |
---|---|
f1ores |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1ssres 5449 |
. . 3
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2 | f1f1orn 5491 |
. . 3
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3 | 1, 2 | syl 14 |
. 2
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4 | df-ima 4657 |
. . 3
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5 | f1oeq3 5470 |
. . 3
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6 | 4, 5 | ax-mp 5 |
. 2
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7 | 3, 6 | sylibr 134 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-fun 5237 df-fn 5238 df-f 5239 df-f1 5240 df-fo 5241 df-f1o 5242 |
This theorem is referenced by: f1imacnv 5497 f1oresrab 5702 isores3 5837 isoini2 5841 f1imaeng 6818 f1imaen2g 6819 preimaf1ofi 6980 endjusym 7125 dju1p1e2 7226 fisumss 11432 fprodssdc 11630 ssnnctlemct 12497 eqgen 13166 |
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