Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > opex | Unicode version |
Description: An ordered pair of sets is a set. (Contributed by Jim Kingdon, 24-Sep-2018.) (Revised by Mario Carneiro, 24-May-2019.) |
Ref | Expression |
---|---|
opex.1 | |
opex.2 |
Ref | Expression |
---|---|
opex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex.1 | . 2 | |
2 | opex.2 | . 2 | |
3 | opexg 3964 | . 2 | |
4 | 1, 2, 3 | mp2an 402 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 cvv 2557 cop 3378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 |
This theorem is referenced by: opabid 3994 elopab 3995 opabm 4017 elvvv 4403 xpiindim 4473 raliunxp 4477 rexiunxp 4478 intirr 4711 xpmlem 4744 dmsnm 4786 dmsnopg 4792 cnvcnvsn 4797 cnviinm 4859 funopg 4934 fsn 5335 idref 5396 oprabid 5537 dfoprab2 5552 rnoprab 5587 fo1st 5784 fo2nd 5785 eloprabi 5822 xporderlem 5852 dmtpos 5871 rntpos 5872 tpostpos 5879 iinerm 6178 th3qlem2 6209 ensn1 6276 xpsnen 6295 xpcomco 6300 xpassen 6304 phplem2 6316 ac6sfi 6352 genipdm 6614 ioof 8840 |
Copyright terms: Public domain | W3C validator |