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Mirrors > Home > ILE Home > Th. List > relss | Unicode version |
Description: Subclass theorem for relation predicate. Theorem 2 of [Suppes] p. 58. (Contributed by NM, 15-Aug-1994.) |
Ref | Expression |
---|---|
relss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sstr2 3104 | . 2 | |
2 | df-rel 4546 | . 2 | |
3 | df-rel 4546 | . 2 | |
4 | 1, 2, 3 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 cvv 2686 wss 3071 cxp 4537 wrel 4544 |
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-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-in 3077 df-ss 3084 df-rel 4546 |
This theorem is referenced by: relin1 4657 relin2 4658 reldif 4659 relres 4847 iss 4865 cnvdif 4945 funss 5142 funssres 5165 fliftcnv 5696 fliftfun 5697 reltpos 6147 tpostpos 6161 swoer 6457 erinxp 6503 ltrel 7826 lerel 7828 txdis1cn 12447 xmeter 12605 |
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