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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 3074 | . 2 | |
2 | df-rel 4516 | . 2 | |
3 | df-rel 4516 | . 2 | |
4 | 1, 2, 3 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 cvv 2660 wss 3041 cxp 4507 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-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 df-rel 4516 |
This theorem is referenced by: relin1 4627 relin2 4628 reldif 4629 relres 4817 iss 4835 cnvdif 4915 funss 5112 funssres 5135 fliftcnv 5664 fliftfun 5665 reltpos 6115 tpostpos 6129 swoer 6425 erinxp 6471 ltrel 7794 lerel 7796 txdis1cn 12374 xmeter 12532 |
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