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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 3229 | . 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 1332 ∪ cun 3074 |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 |
This theorem is referenced by: un4 3241 unundir 3243 difun2 3447 difdifdirss 3452 qdass 3628 qdassr 3629 unisuc 4343 iunsuc 4350 fmptap 5618 fvsnun1 5625 rdgival 6287 rdg0 6292 undifdc 6820 exmidfodomrlemim 7074 djuassen 7090 facnn 10505 fac0 10506 fsum2dlemstep 11235 fsumiun 11278 |
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