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Mirrors > Home > ILE Home > Th. List > uncom | Unicode version |
Description: Commutative law for union of classes. Exercise 6 of [TakeutiZaring] p. 17. (Contributed by NM, 25-Jun-1998.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
uncom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 717 | . . 3 | |
2 | elun 3217 | . . 3 | |
3 | 1, 2 | bitr4i 186 | . 2 |
4 | 3 | uneqri 3218 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 697 wceq 1331 wcel 1480 cun 3069 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 |
This theorem is referenced by: equncom 3221 uneq2 3224 un12 3234 un23 3235 ssun2 3240 unss2 3247 ssequn2 3249 undir 3326 dif32 3339 undif2ss 3438 uneqdifeqim 3448 prcom 3599 tpass 3619 prprc1 3631 difsnss 3666 suc0 4333 fvun2 5488 fmptpr 5612 fvsnun2 5618 fsnunfv 5621 omv2 6361 phplem2 6747 undifdc 6812 endjusym 6981 fzsuc2 9859 fseq1p1m1 9874 ennnfonelem1 11920 setsslid 12009 exmid1stab 13195 |
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