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Mirrors > Home > ILE Home > Th. List > ssimaexg | Unicode version |
Description: The existence of a subimage. (Contributed by FL, 15-Apr-2007.) |
Ref | Expression |
---|---|
ssimaexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imaeq2 4684 | . . . . . 6 | |
2 | 1 | sseq2d 3027 | . . . . 5 |
3 | 2 | anbi2d 451 | . . . 4 |
4 | sseq2 3021 | . . . . . 6 | |
5 | 4 | anbi1d 452 | . . . . 5 |
6 | 5 | exbidv 1746 | . . . 4 |
7 | 3, 6 | imbi12d 232 | . . 3 |
8 | vex 2604 | . . . 4 | |
9 | 8 | ssimaex 5255 | . . 3 |
10 | 7, 9 | vtoclg 2658 | . 2 |
11 | 10 | 3impib 1136 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 w3a 919 wceq 1284 wex 1421 wcel 1433 wss 2973 cima 4366 wfun 4916 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-iota 4887 df-fun 4924 df-fn 4925 df-fv 4930 |
This theorem is referenced by: (None) |
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