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Mirrors > Home > ILE Home > Th. List > brrelex1i | Unicode version |
Description: The first argument of a binary relation exists. (An artifact of our ordered pair definition.) (Contributed by NM, 4-Jun-1998.) |
Ref | Expression |
---|---|
brrelexi.1 |
Ref | Expression |
---|---|
brrelex1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brrelexi.1 | . 2 | |
2 | brrelex1 4548 | . 2 | |
3 | 1, 2 | mpan 420 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 cvv 2660 class class class wbr 3899 wrel 4514 |
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-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 |
This theorem is referenced by: nprrel 4554 vtoclr 4557 opeliunxp2 4649 ideqg 4660 issetid 4663 fvmptss2 5464 opeliunxp2f 6103 brtpos2 6116 brdomg 6610 ctex 6615 isfi 6623 en1uniel 6666 xpdom2 6693 xpdom1g 6695 xpen 6707 isbth 6823 djudom 6946 aprcl 8376 climcl 11019 climi 11024 climrecl 11061 structex 11898 |
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