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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 680 |
. . 3
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2 | elun 3114 |
. . 3
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3 | 1, 2 | bitr4i 185 |
. 2
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4 | 3 | uneqri 3115 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-v 2604 df-un 2978 |
This theorem is referenced by: equncom 3118 uneq2 3121 un12 3131 un23 3132 ssun2 3137 unss2 3144 ssequn2 3146 undir 3221 dif32 3234 undif2ss 3326 uneqdifeqim 3335 prcom 3476 tpass 3496 prprc1 3508 difsnss 3539 suc0 4174 fvun2 5272 fmptpr 5387 fvsnun2 5393 fsnunfv 5395 omv2 6109 phplem2 6388 undiffi 6443 fzsuc2 9172 fseq1p1m1 9187 |
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