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Mirrors > Home > ILE Home > Th. List > prid1 | Unicode version |
Description: An unordered pair contains its first member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
prid1.1 |
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Ref | Expression |
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prid1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prid1.1 |
. 2
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2 | prid1g 3695 |
. 2
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3 | 1, 2 | ax-mp 5 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3597 df-pr 3598 |
This theorem is referenced by: prid2 3698 prnz 3713 preqr1 3766 preq12b 3768 prel12 3769 opi1 4228 opeluu 4446 onsucelsucexmidlem1 4523 regexmidlem1 4528 reg2exmidlema 4529 opthreg 4551 ordtri2or2exmid 4566 ontri2orexmidim 4567 dmrnssfld 4885 funopg 5245 acexmidlemb 5860 0lt2o 6435 2dom 6798 unfiexmid 6910 djuss 7062 exmidomni 7133 exmidonfinlem 7185 exmidaclem 7200 reelprrecn 7924 pnfxr 7987 sup3exmid 8890 lgsdir2lem3 14064 bdop 14249 2o01f 14368 iswomni0 14422 |
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