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Mirrors > Home > ILE Home > Th. List > uniex | Unicode version |
Description: The Axiom of Union in class notation. This says that if is a set i.e. (see isset 2666), then the union of is also a set. Same as Axiom 3 of [TakeutiZaring] p. 16. (Contributed by NM, 11-Aug-1993.) |
Ref | Expression |
---|---|
uniex.1 |
Ref | Expression |
---|---|
uniex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniex.1 | . 2 | |
2 | unieq 3715 | . . 3 | |
3 | 2 | eleq1d 2186 | . 2 |
4 | uniex2 4328 | . . 3 | |
5 | 4 | issetri 2669 | . 2 |
6 | 1, 3, 5 | vtocl 2714 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wcel 1465 cvv 2660 cuni 3706 |
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-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-un 4325 |
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-rex 2399 df-v 2662 df-uni 3707 |
This theorem is referenced by: vuniex 4330 uniexg 4331 unex 4332 uniuni 4342 iunpw 4371 fo1st 6023 fo2nd 6024 brtpos2 6116 tfrexlem 6199 ixpsnf1o 6598 xpcomco 6688 xpassen 6692 pnfnre 7775 pnfxr 7786 |
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