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Mirrors > Home > ILE Home > Th. List > uneq1 | Unicode version |
Description: Equality theorem for union of two classes. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
uneq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2203 | . . . 4 | |
2 | 1 | orbi1d 780 | . . 3 |
3 | elun 3217 | . . 3 | |
4 | elun 3217 | . . 3 | |
5 | 2, 3, 4 | 3bitr4g 222 | . 2 |
6 | 5 | eqrdv 2137 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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: uneq2 3224 uneq12 3225 uneq1i 3226 uneq1d 3229 prprc1 3631 uniprg 3751 unexb 4363 relresfld 5068 relcoi1 5070 rdgeq2 6269 xpider 6500 findcard2 6783 findcard2s 6784 unfiexmid 6806 bdunexb 13118 bj-unexg 13119 exmid1stab 13195 |
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