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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 3182 | . 2 | |
2 | 1 | eqcoms 2160 | 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: disjeq2 3947 disjeq1 3950 poeq2 4261 seeq1 4300 seeq2 4301 dmcoeq 4859 xp11m 5025 funeq 5191 fconst3m 5687 tposeq 6195 undifdcss 6868 ennnfonelemk 12171 ennnfonelemss 12181 qnnen 12202 topgele 12469 topontopn 12477 txdis 12719 |
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