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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 3680 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2136 cvv 2726 cpr 3577 |
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 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-ext 2147 |
This theorem depends on definitions: df-bi 116 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-v 2728 df-un 3120 df-sn 3582 df-pr 3583 |
This theorem is referenced by: prid2 3683 prnz 3698 preqr1 3748 preq12b 3750 prel12 3751 opi1 4210 opeluu 4428 onsucelsucexmidlem1 4505 regexmidlem1 4510 reg2exmidlema 4511 opthreg 4533 ordtri2or2exmid 4548 ontri2orexmidim 4549 dmrnssfld 4867 funopg 5222 acexmidlemb 5834 0lt2o 6409 2dom 6771 unfiexmid 6883 djuss 7035 exmidomni 7106 exmidonfinlem 7149 exmidaclem 7164 reelprrecn 7888 pnfxr 7951 sup3exmid 8852 lgsdir2lem3 13571 bdop 13757 2o01f 13876 iswomni0 13930 |
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