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Mirrors > Home > ILE Home > Th. List > uneq2 | Unicode version |
Description: Equality theorem for the union of two classes. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
uneq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uneq1 3193 | . 2 | |
2 | uncom 3190 | . 2 | |
3 | uncom 3190 | . 2 | |
4 | 1, 2, 3 | 3eqtr4g 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 cun 3039 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 |
This theorem is referenced by: uneq12 3195 uneq2i 3197 uneq2d 3200 uneqin 3297 disjssun 3396 uniprg 3721 sucprc 4304 unexb 4333 unfiexmid 6774 unfidisj 6778 hashunlem 10518 bdunexb 13045 bj-unexg 13046 |
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