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Mirrors > Home > ILE Home > Th. List > eldifn | Unicode version |
Description: Implication of membership in a class difference. (Contributed by NM, 3-May-1994.) |
Ref | Expression |
---|---|
eldifn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 3123 | . 2 | |
2 | 1 | simprbi 273 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wcel 2135 cdif 3111 |
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 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-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2726 df-dif 3116 |
This theorem is referenced by: elndif 3244 unssin 3359 inssun 3360 noel 3411 disjel 3461 undifexmid 4169 exmidundif 4182 exmidundifim 4183 phpm 6825 undifdcss 6882 fsum3cvg 11313 summodclem2a 11316 fisumss 11327 isumss2 11328 binomlem 11418 fproddccvg 11507 prodmodclem2a 11511 fprodssdc 11525 fprodsplitdc 11531 exmid1stab 13773 |
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