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Mirrors > Home > ILE Home > Th. List > sseqtrdi | Unicode version |
Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.) |
Ref | Expression |
---|---|
sseqtrdi.1 | |
sseqtrdi.2 |
Ref | Expression |
---|---|
sseqtrdi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseqtrdi.1 | . 2 | |
2 | sseqtrdi.2 | . . 3 | |
3 | 2 | sseq2i 3174 | . 2 |
4 | 1, 3 | sylib 121 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wss 3121 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-in 3127 df-ss 3134 |
This theorem is referenced by: sseqtrrdi 3196 onintonm 4501 relrelss 5137 iotanul 5175 foimacnv 5460 cauappcvgprlemladdru 7618 zsumdc 11347 fsum3cvg3 11359 zproddc 11542 nninfdcex 11908 zsupssdc 11909 distop 12879 cnptoprest 13033 pwle2 14031 pw1nct 14036 |
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