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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 3297 | . 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 1364 ∪ cun 3142 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 |
This theorem is referenced by: un12 3308 unundi 3311 tpcoma 3701 qdass 3704 qdassr 3705 tpidm12 3706 resasplitss 5414 fmptpr 5728 df2o3 6454 undifdc 6951 sbthlemi6 6990 exmidfodomrlemim 7229 znnen 12448 setscom 12551 |
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