![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > prid2 | Unicode version |
Description: An unordered pair contains its second member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
prid2.1 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
prid2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prid2.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | prid1 3637 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | prcom 3607 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | eleqtri 2215 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 |
This theorem is referenced by: prel12 3706 opi2 4163 opeluu 4379 ontr2exmid 4448 onsucelsucexmid 4453 regexmidlemm 4455 ordtri2or2exmid 4494 dmrnssfld 4810 funopg 5165 acexmidlema 5773 acexmidlemcase 5777 acexmidlem2 5779 1lt2o 6347 2dom 6707 unfiexmid 6814 djuss 6963 exmidonfinlem 7066 exmidfodomrlemr 7075 exmidfodomrlemrALT 7076 exmidaclem 7081 cnelprrecn 7780 mnfxr 7846 sup3exmid 8739 m1expcl2 10346 bdop 13244 2o01f 13364 |
Copyright terms: Public domain | W3C validator |