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| Mirrors > Home > ILE Home > Th. List > imai | Unicode version | ||
| Description: Image under the identity relation. Theorem 3.16(viii) of [Monk1] p. 38. (Contributed by NM, 30-Apr-1998.) |
| Ref | Expression |
|---|---|
| imai |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dfima3 5025 |
. 2
| |
| 2 | df-br 4045 |
. . . . . . . 8
| |
| 3 | vex 2775 |
. . . . . . . . 9
| |
| 4 | 3 | ideq 4830 |
. . . . . . . 8
|
| 5 | 2, 4 | bitr3i 186 |
. . . . . . 7
|
| 6 | 5 | anbi2i 457 |
. . . . . 6
|
| 7 | ancom 266 |
. . . . . 6
| |
| 8 | 6, 7 | bitri 184 |
. . . . 5
|
| 9 | 8 | exbii 1628 |
. . . 4
|
| 10 | eleq1 2268 |
. . . . 5
| |
| 11 | 3, 10 | ceqsexv 2811 |
. . . 4
|
| 12 | 9, 11 | bitri 184 |
. . 3
|
| 13 | 12 | abbii 2321 |
. 2
|
| 14 | abid2 2326 |
. 2
| |
| 15 | 1, 13, 14 | 3eqtri 2230 |
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-un 3170 df-in 3172 df-ss 3179 df-pw 3618 df-sn 3639 df-pr 3640 df-op 3642 df-br 4045 df-opab 4106 df-id 4340 df-xp 4681 df-rel 4682 df-cnv 4683 df-dm 4685 df-rn 4686 df-res 4687 df-ima 4688 |
| This theorem is referenced by: rnresi 5039 cnvresid 5348 ecidsn 6669 |
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