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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 2561), 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 3589 | . . 3 | |
3 | 2 | eleq1d 2106 | . 2 |
4 | uniex2 4173 | . . 3 | |
5 | 4 | issetri 2564 | . 2 |
6 | 1, 3, 5 | vtocl 2608 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 wcel 1393 cvv 2557 cuni 3580 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-un 4170 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-uni 3581 |
This theorem is referenced by: uniexg 4175 unex 4176 uniuni 4183 iunpw 4211 fo1st 5784 fo2nd 5785 brtpos2 5866 tfrexlem 5948 xpcomco 6300 xpassen 6304 pnfnre 7067 pnfxr 8692 |
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