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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 3138. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
eldifbd.1 |
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Ref | Expression |
---|---|
eldifbd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldifbd.1 |
. . 3
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2 | eldif 3138 |
. . 3
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3 | 1, 2 | sylib 122 |
. 2
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4 | 3 | simprd 114 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-dif 3131 |
This theorem is referenced by: fidifsnen 6869 fiunsnnn 6880 fimax2gtri 6900 unfidisj 6920 ssfirab 6932 fnfi 6935 iunfidisj 6944 hashunlem 10779 hashxp 10801 zfz1isolemiso 10814 fsumconst 11457 fsumrelem 11474 fprodcl2lem 11608 fprodconst 11623 fprodap0 11624 fprodrec 11632 fprodap0f 11639 fprodle 11643 fprodmodd 11644 fsumcncntop 13949 bj-charfun 14441 bj-charfundc 14442 |
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