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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 3467 |
. 2
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3 | prcom 3437 |
. 2
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4 | 2, 3 | eleqtri 2109 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-un 2916 df-sn 3373 df-pr 3374 |
This theorem is referenced by: prel12 3533 opi2 3961 opeluu 4148 onsucelsucexmid 4215 regexmidlemm 4217 dmrnssfld 4538 funopg 4877 acexmidlema 5446 acexmidlemcase 5450 acexmidlem2 5452 2dom 6221 cnelprrecn 6815 mnfxr 8464 m1expcl2 8931 bdop 9330 |
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