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Mirrors > Home > ILE Home > Th. List > unex | Unicode version |
Description: The union of two sets is a set. Corollary 5.8 of [TakeutiZaring] p. 16. (Contributed by NM, 1-Jul-1994.) |
Ref | Expression |
---|---|
unex.1 | |
unex.2 |
Ref | Expression |
---|---|
unex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unex.1 | . . 3 | |
2 | unex.2 | . . 3 | |
3 | 1, 2 | unipr 3745 | . 2 |
4 | prexg 4128 | . . . 4 | |
5 | 1, 2, 4 | mp2an 422 | . . 3 |
6 | 5 | uniex 4354 | . 2 |
7 | 3, 6 | eqeltrri 2211 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cvv 2681 cun 3064 cpr 3523 cuni 3731 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pr 4126 ax-un 4350 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-uni 3732 |
This theorem is referenced by: unexb 4358 rdg0 6277 unen 6703 findcard2 6776 findcard2s 6777 ac6sfi 6785 sbthlemi10 6847 finomni 7005 exmidfodomrlemim 7050 nn0ex 8976 xrex 9632 exmidunben 11928 strleun 12037 |
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