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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 3615 | . 2 |
4 | prexg 3966 | . . . 4 | |
5 | 1, 2, 4 | mp2an 416 | . . 3 |
6 | 5 | uniex 4192 | . 2 |
7 | 3, 6 | eqeltrri 2152 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1433 cvv 2601 cun 2971 cpr 3399 cuni 3601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pr 3964 ax-un 4188 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-uni 3602 |
This theorem is referenced by: unexb 4195 rdg0 5997 unen 6316 findcard2 6373 findcard2s 6374 ac6sfi 6379 nn0ex 8294 xrex 8910 |
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