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Mirrors > Home > ILE Home > Th. List > f1ocnvfv1 | Unicode version |
Description: The converse value of the value of a one-to-one onto function. (Contributed by NM, 20-May-2004.) |
Ref | Expression |
---|---|
f1ocnvfv1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1ococnv1 5509 |
. . . 4
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2 | 1 | fveq1d 5536 |
. . 3
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3 | 2 | adantr 276 |
. 2
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4 | f1of 5480 |
. . 3
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5 | fvco3 5608 |
. . 3
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6 | 4, 5 | sylan 283 |
. 2
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7 | fvresi 5730 |
. . 3
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8 | 7 | adantl 277 |
. 2
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9 | 3, 6, 8 | 3eqtr3d 2230 |
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-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-id 4311 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-iota 5196 df-fun 5237 df-fn 5238 df-f 5239 df-f1 5240 df-fo 5241 df-f1o 5242 df-fv 5243 |
This theorem is referenced by: f1ocnvfv 5801 caseinl 7121 caseinr 7122 ctssdccl 7141 cc3 7298 iseqf1olemab 10522 cnrecnv 10954 fprodssdc 11633 ennnfonelemhf1o 12467 ennnfonelemex 12468 ennnfonelemrn 12473 ctinfomlemom 12481 ssnnctlemct 12500 mhmf1o 12937 isomninnlem 15257 iswomninnlem 15276 ismkvnnlem 15279 |
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