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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 3808 | . 2 |
4 | prexg 4194 | . . . 4 | |
5 | 1, 2, 4 | mp2an 424 | . . 3 |
6 | 5 | uniex 4420 | . 2 |
7 | 3, 6 | eqeltrri 2244 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2141 cvv 2730 cun 3119 cpr 3582 cuni 3794 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pr 4192 ax-un 4416 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-un 3125 df-sn 3587 df-pr 3588 df-uni 3795 |
This theorem is referenced by: unexb 4425 rdg0 6364 unen 6791 findcard2 6864 findcard2s 6865 ac6sfi 6873 sbthlemi10 6940 finomni 7113 exmidfodomrlemim 7167 nn0ex 9130 xrex 9802 exmidunben 12370 strleun 12496 |
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