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Mirrors > Home > ILE Home > Th. List > cc4 | Unicode version |
Description: Countable choice by
showing the existence of a function ![]() ![]() ![]() |
Ref | Expression |
---|---|
cc4.cc |
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cc4.1 |
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cc4.2 |
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cc4.3 |
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cc4.m |
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Ref | Expression |
---|---|
cc4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cc4.cc |
. 2
![]() ![]() ![]() ![]() ![]() | |
2 | cc4.1 |
. 2
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3 | nfcv 2296 |
. 2
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4 | cc4.2 |
. 2
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5 | cc4.3 |
. 2
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6 | cc4.m |
. 2
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7 | 1, 2, 3, 4, 5, 6 | cc4f 7168 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-13 2127 ax-14 2128 ax-ext 2136 ax-coll 4075 ax-sep 4078 ax-pow 4130 ax-pr 4164 ax-un 4388 ax-iinf 4541 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1740 df-eu 2006 df-mo 2007 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-ral 2437 df-rex 2438 df-reu 2439 df-rab 2441 df-v 2711 df-sbc 2934 df-csb 3028 df-un 3102 df-in 3104 df-ss 3111 df-pw 3541 df-sn 3562 df-pr 3563 df-op 3565 df-uni 3769 df-int 3804 df-iun 3847 df-br 3962 df-opab 4022 df-mpt 4023 df-id 4248 df-iom 4544 df-xp 4585 df-rel 4586 df-cnv 4587 df-co 4588 df-dm 4589 df-rn 4590 df-res 4591 df-ima 4592 df-iota 5128 df-fun 5165 df-fn 5166 df-f 5167 df-f1 5168 df-fo 5169 df-f1o 5170 df-fv 5171 df-2nd 6079 df-er 6469 df-en 6675 df-cc 7162 |
This theorem is referenced by: (None) |
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