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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 |
Ref | Expression |
---|---|
prid1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prid1.1 | . 2 | |
2 | prid1g 3597 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 cvv 2660 cpr 3498 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 |
This theorem is referenced by: prid2 3600 prnz 3615 preqr1 3665 preq12b 3667 prel12 3668 opi1 4124 opeluu 4341 onsucelsucexmidlem1 4413 regexmidlem1 4418 reg2exmidlema 4419 opthreg 4441 ordtri2or2exmid 4456 dmrnssfld 4772 funopg 5127 acexmidlemb 5734 0lt2o 6306 2dom 6667 unfiexmid 6774 djuss 6923 exmidomni 6982 exmidonfinlem 7017 exmidaclem 7032 reelprrecn 7723 pnfxr 7786 sup3exmid 8683 bdop 13000 isomninnlem 13152 |
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