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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 3176 |
. 2
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2 | df-rel 4647 |
. 2
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3 | df-rel 4647 |
. 2
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4 | 1, 2, 3 | 3imtr4g 205 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-11 1516 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2170 |
This theorem depends on definitions: df-bi 117 df-nf 1471 df-sb 1773 df-clab 2175 df-cleq 2181 df-clel 2184 df-in 3149 df-ss 3156 df-rel 4647 |
This theorem is referenced by: relin1 4758 relin2 4759 reldif 4760 relres 4949 iss 4967 cnvdif 5049 funss 5249 funssres 5272 fliftcnv 5811 fliftfun 5812 reltpos 6268 tpostpos 6282 swoer 6580 erinxp 6626 ltrel 8036 lerel 8038 txdis1cn 14161 xmeter 14319 |
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