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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 3185 |
. 2
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2 | 1 | simplbi 274 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-in 3150 df-ss 3157 |
This theorem is referenced by: eqimss2 3225 uneqin 3401 sssnr 3768 sssnm 3769 ssprr 3771 sstpr 3772 snsspw 3779 pwpwssunieq 3990 elpwuni 3991 disjeq2 3999 disjeq1 4002 pwne 4178 pwssunim 4302 poeq2 4318 seeq1 4357 seeq2 4358 trsucss 4441 onsucelsucr 4525 xp11m 5085 funeq 5255 fnresdm 5344 fssxp 5402 ffdm 5405 fcoi1 5415 fof 5457 dff1o2 5485 fvmptss2 5612 fvmptssdm 5621 fprg 5720 dff1o6 5798 tposeq 6273 el2oss1o 6469 nntri1 6522 nntri2or2 6524 nnsseleq 6527 infnninf 7153 infnninfOLD 7154 nninfwlpoimlemg 7204 exmidontri2or 7273 frec2uzf1od 10439 hashinfuni 10792 setsresg 12553 setsslid 12566 strle1g 12621 cncnpi 14205 hmeores 14292 limcimolemlt 14610 recnprss 14633 0nninf 15232 nninfall 15237 |
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