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Mirrors > Home > NFE Home > Th. List > unidm | GIF version |
Description: Idempotent law for union of classes. Theorem 23 of [Suppes] p. 27. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
unidm | ⊢ (A ∪ A) = A |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oridm 500 | . 2 ⊢ ((x ∈ A ∨ x ∈ A) ↔ x ∈ A) | |
2 | 1 | uneqri 3406 | 1 ⊢ (A ∪ A) = A |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1642 ∈ wcel 1710 ∪ cun 3207 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 |
This theorem is referenced by: unundi 3424 unundir 3425 uneqin 3506 difabs 3518 undifabs 3627 dfif5 3674 dfsn2 3747 diftpsn3 3849 unisn 3907 |
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