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Mirrors > Home > ILE Home > Th. List > eqimss2 | Unicode version |
Description: Equality implies the subclass relation. (Contributed by NM, 23-Nov-2003.) |
Ref | Expression |
---|---|
eqimss2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss 3201 | . 2 | |
2 | 1 | eqcoms 2173 | 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: disjeq2 3970 disjeq1 3973 poeq2 4285 seeq1 4324 seeq2 4325 dmcoeq 4883 xp11m 5049 funeq 5218 fconst3m 5715 tposeq 6226 undifdcss 6900 ennnfonelemk 12355 ennnfonelemss 12365 qnnen 12386 topgele 12821 topontopn 12829 txdis 13071 |
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