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Mirrors > Home > ILE Home > Th. List > uneq2i | GIF version |
Description: Inference adding union to the left in a class equality. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
uneq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
uneq2i | ⊢ (𝐶 ∪ 𝐴) = (𝐶 ∪ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uneq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | uneq2 3194 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶 ∪ 𝐴) = (𝐶 ∪ 𝐵)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐶 ∪ 𝐴) = (𝐶 ∪ 𝐵) |
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: un4 3206 unundir 3208 difun2 3412 difdifdirss 3417 qdass 3590 qdassr 3591 unisuc 4305 iunsuc 4312 fmptap 5578 fvsnun1 5585 rdgival 6247 rdg0 6252 undifdc 6780 exmidfodomrlemim 7025 djuassen 7041 facnn 10441 fac0 10442 fsum2dlemstep 11171 fsumiun 11214 |
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