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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 |
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Ref | Expression |
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prid2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prid2.1 |
. . 3
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2 | 1 | prid1 3724 |
. 2
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3 | prcom 3694 |
. 2
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4 | 2, 3 | eleqtri 2268 |
1
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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-ext 2175 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 df-un 3157 df-sn 3624 df-pr 3625 |
This theorem is referenced by: prel12 3797 opi2 4262 opeluu 4481 ontr2exmid 4557 onsucelsucexmid 4562 regexmidlemm 4564 ordtri2or2exmid 4603 ontri2orexmidim 4604 dmrnssfld 4925 funopg 5288 acexmidlema 5909 acexmidlemcase 5913 acexmidlem2 5915 1lt2o 6495 2dom 6859 unfiexmid 6974 djuss 7129 exmidonfinlem 7253 exmidfodomrlemr 7262 exmidfodomrlemrALT 7263 exmidaclem 7268 cnelprrecn 8008 mnfxr 8076 sup3exmid 8976 m1expcl2 10632 fnpr2ob 12923 lgsdir2lem3 15146 bdop 15367 2o01f 15487 iswomni0 15541 |
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