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Mirrors > Home > ILE Home > Th. List > eldifbd | Unicode version |
Description: If a class is in the difference of two classes, it is not in the subtrahend. One-way deduction form of eldif 3111. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
eldifbd.1 |
Ref | Expression |
---|---|
eldifbd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldifbd.1 | . . 3 | |
2 | eldif 3111 | . . 3 | |
3 | 1, 2 | sylib 121 | . 2 |
4 | 3 | simprd 113 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wcel 2128 cdif 3099 |
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-in1 604 ax-in2 605 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-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-dif 3104 |
This theorem is referenced by: fidifsnen 6815 fiunsnnn 6826 fimax2gtri 6846 unfidisj 6866 ssfirab 6878 fnfi 6881 iunfidisj 6890 hashunlem 10678 hashxp 10700 zfz1isolemiso 10710 fsumconst 11351 fsumrelem 11368 fprodcl2lem 11502 fprodconst 11517 fprodap0 11518 fprodrec 11526 fprodap0f 11533 fprodle 11537 fprodmodd 11538 fsumcncntop 12956 bj-charfun 13382 bj-charfundc 13383 |
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