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Mirrors > Home > ILE Home > Th. List > resima2 | Unicode version |
Description: Image under a restricted class. (Contributed by FL, 31-Aug-2009.) |
Ref | Expression |
---|---|
resima2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ima 4624 | . 2 | |
2 | resres 4903 | . . . 4 | |
3 | 2 | rneqi 4839 | . . 3 |
4 | df-ss 3134 | . . . 4 | |
5 | incom 3319 | . . . . . . . 8 | |
6 | 5 | a1i 9 | . . . . . . 7 |
7 | 6 | reseq2d 4891 | . . . . . 6 |
8 | 7 | rneqd 4840 | . . . . 5 |
9 | reseq2 4886 | . . . . . . 7 | |
10 | 9 | rneqd 4840 | . . . . . 6 |
11 | df-ima 4624 | . . . . . 6 | |
12 | 10, 11 | eqtr4di 2221 | . . . . 5 |
13 | 8, 12 | eqtrd 2203 | . . . 4 |
14 | 4, 13 | sylbi 120 | . . 3 |
15 | 3, 14 | eqtrid 2215 | . 2 |
16 | 1, 15 | eqtrid 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 cin 3120 wss 3121 crn 4612 cres 4613 cima 4614 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-xp 4617 df-rel 4618 df-cnv 4619 df-dm 4621 df-rn 4622 df-res 4623 df-ima 4624 |
This theorem is referenced by: cnptopresti 13032 cnptoprest 13033 |
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