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Mirrors > Home > ILE Home > Th. List > eqimss | Unicode version |
Description: Equality implies the subclass relation. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 21-Jun-2011.) |
Ref | Expression |
---|---|
eqimss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqss 3040 |
. 2
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2 | 1 | simplbi 268 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-11 1442 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-in 3005 df-ss 3012 |
This theorem is referenced by: eqimss2 3079 uneqin 3250 sssnr 3595 sssnm 3596 ssprr 3598 sstpr 3599 snsspw 3606 pwpwssunieq 3815 elpwuni 3816 disjeq2 3824 disjeq1 3827 pwne 3993 pwssunim 4109 poeq2 4125 seeq1 4164 seeq2 4165 trsucss 4248 onsucelsucr 4323 xp11m 4864 funeq 5029 fnresdm 5117 fssxp 5172 ffdm 5175 fcoi1 5185 fof 5227 dff1o2 5252 fvmptss2 5373 fvmptssdm 5381 fprg 5474 dff1o6 5547 tposeq 6004 nntri1 6249 nntri2or2 6251 nnsseleq 6254 infnninf 6795 frec2uzf1od 9801 hashinfuni 10173 el2oss1o 11770 0nninf 11776 nninfall 11783 |
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