Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rbropap | Unicode version |
Description: Properties of a pair in a restricted binary relation expressed as an ordered-pair class abstraction: is the binary relation restricted by the condition . (Contributed by AV, 31-Jan-2021.) |
Ref | Expression |
---|---|
rbropapd.1 | |
rbropapd.2 |
Ref | Expression |
---|---|
rbropap |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rbropapd.1 | . . 3 | |
2 | rbropapd.2 | . . 3 | |
3 | 1, 2 | rbropapd 6139 | . 2 |
4 | 3 | 3impib 1179 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wceq 1331 wcel 1480 class class class wbr 3929 copab 3988 |
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 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |