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Mirrors > Home > ILE Home > Th. List > sseq12i | Unicode version |
Description: An equality inference for the subclass relationship. (Contributed by NM, 31-May-1999.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
sseq1i.1 | |
sseq12i.2 |
Ref | Expression |
---|---|
sseq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1i.1 | . 2 | |
2 | sseq12i.2 | . 2 | |
3 | sseq12 3022 | . 2 | |
4 | 1, 2, 3 | mp2an 416 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 103 wceq 1284 wss 2973 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-in 2979 df-ss 2986 |
This theorem is referenced by: 3sstr3i 3037 3sstr4i 3038 3sstr3g 3039 3sstr4g 3040 ss2rab 3070 |
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