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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sstr2 3070 |
. 2
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2 | df-rel 4506 |
. 2
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3 | df-rel 4506 |
. 2
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4 | 1, 2, 3 | 3imtr4g 204 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-11 1467 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-in 3043 df-ss 3050 df-rel 4506 |
This theorem is referenced by: relin1 4617 relin2 4618 reldif 4619 relres 4805 iss 4823 cnvdif 4903 funss 5100 funssres 5123 fliftcnv 5650 fliftfun 5651 reltpos 6101 tpostpos 6115 swoer 6411 erinxp 6457 ltrel 7750 lerel 7752 txdis1cn 12289 xmeter 12425 |
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