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| Mirrors > Home > ILE Home > Th. List > f1ocnvfvb | Unicode version | ||
| Description: Relationship between the value of a one-to-one onto function and the value of its converse. (Contributed by NM, 20-May-2004.) |
| Ref | Expression |
|---|---|
| f1ocnvfvb |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | f1ocnvfv 5848 |
. . 3
| |
| 2 | 1 | 3adant3 1020 |
. 2
|
| 3 | fveq2 5576 |
. . . . 5
| |
| 4 | 3 | eqcoms 2208 |
. . . 4
|
| 5 | f1ocnvfv2 5847 |
. . . . 5
| |
| 6 | 5 | eqeq2d 2217 |
. . . 4
|
| 7 | 4, 6 | imbitrid 154 |
. . 3
|
| 8 | 7 | 3adant2 1019 |
. 2
|
| 9 | 2, 8 | impbid 129 |
1
|
| 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 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-14 2179 ax-ext 2187 ax-sep 4162 ax-pow 4218 ax-pr 4253 |
| This theorem depends on definitions: df-bi 117 df-3an 983 df-tru 1376 df-nf 1484 df-sb 1786 df-eu 2057 df-mo 2058 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-ral 2489 df-rex 2490 df-v 2774 df-sbc 2999 df-un 3170 df-in 3172 df-ss 3179 df-pw 3618 df-sn 3639 df-pr 3640 df-op 3642 df-uni 3851 df-br 4045 df-opab 4106 df-id 4340 df-xp 4681 df-rel 4682 df-cnv 4683 df-co 4684 df-dm 4685 df-rn 4686 df-res 4687 df-ima 4688 df-iota 5232 df-fun 5273 df-fn 5274 df-f 5275 df-f1 5276 df-fo 5277 df-f1o 5278 df-fv 5279 |
| This theorem is referenced by: f1ofveu 5932 f1ocnvfv3 5933 seq3f1olemstep 10659 1arith2 12691 ennnfonelem1 12778 txhmeo 14791 |
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