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Mirrors > Home > ILE Home > Th. List > cc2 | Unicode version |
Description: Countable choice using sequences instead of countable sets. (Contributed by Jim Kingdon, 27-Apr-2024.) |
Ref | Expression |
---|---|
cc2.cc | CCHOICE |
cc2.a | |
cc2.m |
Ref | Expression |
---|---|
cc2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cc2.cc | . 2 CCHOICE | |
2 | cc2.a | . 2 | |
3 | cc2.m | . . . 4 | |
4 | fveq2 5421 | . . . . . . 7 | |
5 | 4 | eleq2d 2209 | . . . . . 6 |
6 | 5 | exbidv 1797 | . . . . 5 |
7 | 6 | cbvralv 2654 | . . . 4 |
8 | 3, 7 | sylib 121 | . . 3 |
9 | eleq1w 2200 | . . . . 5 | |
10 | 9 | cbvexv 1890 | . . . 4 |
11 | 10 | ralbii 2441 | . . 3 |
12 | 8, 11 | sylib 121 | . 2 |
13 | nfcv 2281 | . . 3 | |
14 | nfcv 2281 | . . 3 | |
15 | sneq 3538 | . . . 4 | |
16 | fveq2 5421 | . . . 4 | |
17 | 15, 16 | xpeq12d 4564 | . . 3 |
18 | 13, 14, 17 | cbvmpt 4023 | . 2 |
19 | nfcv 2281 | . . 3 | |
20 | nfcv 2281 | . . . 4 | |
21 | nfcv 2281 | . . . . 5 | |
22 | nffvmpt1 5432 | . . . . 5 | |
23 | 21, 22 | nffv 5431 | . . . 4 |
24 | 20, 23 | nffv 5431 | . . 3 |
25 | 2fveq3 5426 | . . . 4 | |
26 | 25 | fveq2d 5425 | . . 3 |
27 | 19, 24, 26 | cbvmpt 4023 | . 2 |
28 | 1, 2, 12, 18, 27 | cc2lem 7081 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1468 wcel 1480 wral 2416 csn 3527 cmpt 3989 com 4504 cxp 4537 wfn 5118 cfv 5123 c2nd 6037 CCHOICEwacc 7077 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-coll 4043 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-iinf 4502 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-iom 4505 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 df-2nd 6039 df-er 6429 df-en 6635 df-cc 7078 |
This theorem is referenced by: cc3 7083 |
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