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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 4600 | . 2 | |
2 | resres 4879 | . . . 4 | |
3 | 2 | rneqi 4815 | . . 3 |
4 | df-ss 3115 | . . . 4 | |
5 | incom 3299 | . . . . . . . 8 | |
6 | 5 | a1i 9 | . . . . . . 7 |
7 | 6 | reseq2d 4867 | . . . . . 6 |
8 | 7 | rneqd 4816 | . . . . 5 |
9 | reseq2 4862 | . . . . . . 7 | |
10 | 9 | rneqd 4816 | . . . . . 6 |
11 | df-ima 4600 | . . . . . 6 | |
12 | 10, 11 | eqtr4di 2208 | . . . . 5 |
13 | 8, 12 | eqtrd 2190 | . . . 4 |
14 | 4, 13 | sylbi 120 | . . 3 |
15 | 3, 14 | syl5eq 2202 | . 2 |
16 | 1, 15 | syl5eq 2202 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 cin 3101 wss 3102 crn 4588 cres 4589 cima 4590 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-opab 4027 df-xp 4593 df-rel 4594 df-cnv 4595 df-dm 4597 df-rn 4598 df-res 4599 df-ima 4600 |
This theorem is referenced by: cnptopresti 12680 cnptoprest 12681 |
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