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Mirrors > Home > ILE Home > Th. List > eldifad | Unicode version |
Description: If a class is in the difference of two classes, it is also in the minuend. One-way deduction form of eldif 3130. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
eldifad.1 |
Ref | Expression |
---|---|
eldifad |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldifad.1 | . . 3 | |
2 | eldif 3130 | . . 3 | |
3 | 1, 2 | sylib 121 | . 2 |
4 | 3 | simpld 111 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wcel 2141 cdif 3118 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-dif 3123 |
This theorem is referenced by: fimax2gtri 6879 finexdc 6880 unfidisj 6899 undifdc 6901 ssfirab 6911 fnfi 6914 iunfidisj 6923 dcfi 6958 hashunlem 10739 zfz1isolemiso 10774 fsumrelem 11434 fprodcl2lem 11568 fprodap0 11584 fprodrec 11592 fprodap0f 11599 fprodle 11603 iuncld 12909 fsumcncntop 13350 bj-charfun 13842 |
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