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Mirrors > Home > ILE Home > Th. List > eqimssi | Unicode version |
Description: Infer subclass relationship from equality. (Contributed by NM, 6-Jan-2007.) |
Ref | Expression |
---|---|
eqimssi.1 |
Ref | Expression |
---|---|
eqimssi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3112 | . 2 | |
2 | eqimssi.1 | . 2 | |
3 | 1, 2 | sseqtri 3126 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wss 3066 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-in 3072 df-ss 3079 |
This theorem is referenced by: funi 5150 fpr 5595 elfzo1 9960 sumsplitdc 11194 isumlessdc 11258 |
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