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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 728 |
. . 3
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2 | elun 3276 |
. . 3
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3 | 1, 2 | bitr4i 187 |
. 2
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4 | 3 | uneqri 3277 |
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-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-un 3133 |
This theorem is referenced by: equncom 3280 uneq2 3283 un12 3293 un23 3294 ssun2 3299 unss2 3306 ssequn2 3308 undir 3385 dif32 3398 undif2ss 3498 uneqdifeqim 3508 prcom 3668 tpass 3688 prprc1 3700 difsnss 3738 exmid1stab 4208 suc0 4411 fvun2 5583 fmptpr 5708 fvsnun2 5714 fsnunfv 5717 omv2 6465 phplem2 6852 undifdc 6922 endjusym 7094 fzsuc2 10076 fseq1p1m1 10091 ennnfonelem1 12402 setsslid 12507 |
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