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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 3155 | . 2 |
4 | 1, 3 | sylib 121 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wss 3102 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-in 3108 df-ss 3115 |
This theorem is referenced by: sseqtrrdi 3177 onintonm 4477 relrelss 5113 iotanul 5151 foimacnv 5433 cauappcvgprlemladdru 7577 zsumdc 11285 fsum3cvg3 11297 zproddc 11480 nninfdcex 11843 distop 12527 cnptoprest 12681 pwle2 13612 pw1nct 13617 |
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