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Mirrors > Home > ILE Home > Th. List > incom | Unicode version |
Description: Commutative law for intersection of classes. Exercise 7 of [TakeutiZaring] p. 17. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
incom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 264 | . . 3 | |
2 | elin 3301 | . . 3 | |
3 | elin 3301 | . . 3 | |
4 | 1, 2, 3 | 3bitr4i 211 | . 2 |
5 | 4 | eqriv 2161 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1342 wcel 2135 cin 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-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 2724 df-in 3118 |
This theorem is referenced by: ineq2 3313 dfss1 3322 in12 3329 in32 3330 in13 3331 in31 3332 inss2 3339 sslin 3344 inss 3348 indif1 3363 indifcom 3364 indir 3367 symdif1 3383 dfrab2 3393 0in 3440 disjr 3454 ssdifin0 3486 difdifdirss 3489 uneqdifeqim 3490 diftpsn3 3709 iunin1 3925 iinin1m 3930 riinm 3933 rintm 3953 inex2 4112 onintexmid 4545 resiun1 4898 dmres 4900 rescom 4904 resima2 4913 xpssres 4914 resindm 4921 resdmdfsn 4922 resopab 4923 imadisj 4961 ndmima 4976 intirr 4985 djudisj 5026 imainrect 5044 dmresv 5057 resdmres 5090 funimaexg 5267 fnresdisj 5293 fnimaeq0 5304 resasplitss 5362 f0rn0 5377 fvun2 5548 ressnop0 5661 fvsnun1 5677 fsnunfv 5681 offres 6096 smores3 6253 phplem2 6811 unfiin 6883 xpfi 6887 endjusym 7053 djucomen 7164 fzpreddisj 9997 fseq1p1m1 10020 hashunlem 10707 zfz1isolem1 10743 fprodsplit 11528 znnen 12294 setsfun 12392 setsfun0 12393 setsslid 12407 restin 12743 metreslem 12947 bdinex2 13644 |
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