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Mirrors > Home > ILE Home > Th. List > brrelex2i | Unicode version |
Description: The second argument of a binary relation exists. (An artifact of our ordered pair definition.) (Contributed by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
brrelexi.1 |
Ref | Expression |
---|---|
brrelex2i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brrelexi.1 | . 2 | |
2 | brrelex2 4575 | . 2 | |
3 | 1, 2 | mpan 420 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 cvv 2681 class class class wbr 3924 wrel 4539 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-xp 4540 df-rel 4541 |
This theorem is referenced by: vtoclr 4582 brdomi 6636 xpdom2 6718 xpdom1g 6720 mapdom1g 6734 djudom 6971 difinfsn 6978 enomnilem 7003 djuenun 7061 aprcl 8401 hashinfom 10517 clim 11043 ntrivcvgap0 11311 |
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