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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 3797 | . 2 |
4 | prexg 4183 | . . . 4 | |
5 | 1, 2, 4 | mp2an 423 | . . 3 |
6 | 5 | uniex 4409 | . 2 |
7 | 3, 6 | eqeltrri 2238 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2135 cvv 2721 cun 3109 cpr 3571 cuni 3783 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pr 4181 ax-un 4405 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-v 2723 df-un 3115 df-sn 3576 df-pr 3577 df-uni 3784 |
This theorem is referenced by: unexb 4414 rdg0 6346 unen 6773 findcard2 6846 findcard2s 6847 ac6sfi 6855 sbthlemi10 6922 finomni 7095 exmidfodomrlemim 7148 nn0ex 9111 xrex 9783 exmidunben 12302 strleun 12426 |
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