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Mirrors > Home > ILE Home > Th. List > uneq1i | GIF version |
Description: Inference adding union to the right in a class equality. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
uneq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
uneq1i | ⊢ (𝐴 ∪ 𝐶) = (𝐵 ∪ 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uneq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | uneq1 3193 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴 ∪ 𝐶) = (𝐵 ∪ 𝐶)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 ∪ 𝐶) = (𝐵 ∪ 𝐶) |
Colors of variables: wff set class |
Syntax hints: = 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: un12 3204 unundi 3207 tpcoma 3587 qdass 3590 qdassr 3591 tpidm12 3592 resasplitss 5272 fmptpr 5580 df2o3 6295 undifdc 6780 sbthlemi6 6818 exmidfodomrlemim 7025 znnen 11838 setscom 11926 |
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