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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 2952 | . 2 | |
2 | df-rel 4352 | . 2 | |
3 | df-rel 4352 | . 2 | |
4 | 1, 2, 3 | 3imtr4g 194 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 cvv 2557 wss 2917 cxp 4343 wrel 4350 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-in 2924 df-ss 2931 df-rel 4352 |
This theorem is referenced by: relin1 4455 relin2 4456 reldif 4457 relres 4639 iss 4654 cnvdif 4730 funss 4920 funssres 4942 fliftcnv 5435 fliftfun 5436 reltpos 5865 tpostpos 5879 swoer 6134 erinxp 6180 ltrel 7081 lerel 7083 |
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