Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 5480 | . . . . . . 7 | |
5 | 4 | eleq2d 2234 | . . . . . 6 |
6 | 5 | exbidv 1812 | . . . . 5 |
7 | 6 | cbvralv 2689 | . . . 4 |
8 | 3, 7 | sylib 121 | . . 3 |
9 | eleq1w 2225 | . . . . 5 | |
10 | 9 | cbvexv 1905 | . . . 4 |
11 | 10 | ralbii 2470 | . . 3 |
12 | 8, 11 | sylib 121 | . 2 |
13 | nfcv 2306 | . . 3 | |
14 | nfcv 2306 | . . 3 | |
15 | sneq 3581 | . . . 4 | |
16 | fveq2 5480 | . . . 4 | |
17 | 15, 16 | xpeq12d 4623 | . . 3 |
18 | 13, 14, 17 | cbvmpt 4071 | . 2 |
19 | nfcv 2306 | . . 3 | |
20 | nfcv 2306 | . . . 4 | |
21 | nfcv 2306 | . . . . 5 | |
22 | nffvmpt1 5491 | . . . . 5 | |
23 | 21, 22 | nffv 5490 | . . . 4 |
24 | 20, 23 | nffv 5490 | . . 3 |
25 | 2fveq3 5485 | . . . 4 | |
26 | 25 | fveq2d 5484 | . . 3 |
27 | 19, 24, 26 | cbvmpt 4071 | . 2 |
28 | 1, 2, 12, 18, 27 | cc2lem 7198 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1479 wcel 2135 wral 2442 csn 3570 cmpt 4037 com 4561 cxp 4596 wfn 5177 cfv 5182 c2nd 6099 CCHOICEwacc 7194 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-coll 4091 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-iinf 4559 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-reu 2449 df-rab 2451 df-v 2723 df-sbc 2947 df-csb 3041 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-iun 3862 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-iom 4562 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-res 4610 df-ima 4611 df-iota 5147 df-fun 5184 df-fn 5185 df-f 5186 df-f1 5187 df-fo 5188 df-f1o 5189 df-fv 5190 df-2nd 6101 df-er 6492 df-en 6698 df-cc 7195 |
This theorem is referenced by: cc3 7200 |
Copyright terms: Public domain | W3C validator |