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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 3087 | . 2 | |
2 | eqimssi.1 | . 2 | |
3 | 1, 2 | sseqtri 3101 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wss 3041 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 |
This theorem is referenced by: funi 5125 fpr 5570 elfzo1 9935 sumsplitdc 11169 isumlessdc 11233 |
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