![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 3838 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | prexg 4229 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 1, 2, 4 | mp2an 426 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 5 | uniex 4455 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 3, 6 | eqeltrri 2263 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pr 4227 ax-un 4451 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-v 2754 df-un 3148 df-sn 3613 df-pr 3614 df-uni 3825 |
This theorem is referenced by: unexb 4460 rdg0 6412 unen 6842 findcard2 6917 findcard2s 6918 ac6sfi 6926 sbthlemi10 6995 finomni 7168 exmidfodomrlemim 7230 nn0ex 9212 xrex 9886 exmidunben 12477 strleun 12616 fnpsr 13945 |
Copyright terms: Public domain | W3C validator |