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Mirrors > Home > ILE Home > Th. List > equncomi | GIF version |
Description: Inference form of equncom 3253. (Contributed by Alan Sare, 18-Feb-2012.) |
Ref | Expression |
---|---|
equncomi.1 | ⊢ 𝐴 = (𝐵 ∪ 𝐶) |
Ref | Expression |
---|---|
equncomi | ⊢ 𝐴 = (𝐶 ∪ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equncomi.1 | . 2 ⊢ 𝐴 = (𝐵 ∪ 𝐶) | |
2 | equncom 3253 | . 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵)) | |
3 | 1, 2 | mpbi 144 | 1 ⊢ 𝐴 = (𝐶 ∪ 𝐵) |
Colors of variables: wff set class |
Syntax hints: = wceq 1335 ∪ cun 3100 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 |
This theorem is referenced by: disjssun 3458 difprsn1 3697 unidmrn 5121 phplem1 6800 djucomen 7154 |
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