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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 3117 |
. 2
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2 | 1 | simplbi 272 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-in 3082 df-ss 3089 |
This theorem is referenced by: eqimss2 3157 uneqin 3332 sssnr 3688 sssnm 3689 ssprr 3691 sstpr 3692 snsspw 3699 pwpwssunieq 3909 elpwuni 3910 disjeq2 3918 disjeq1 3921 pwne 4092 pwssunim 4214 poeq2 4230 seeq1 4269 seeq2 4270 trsucss 4353 onsucelsucr 4432 xp11m 4985 funeq 5151 fnresdm 5240 fssxp 5298 ffdm 5301 fcoi1 5311 fof 5353 dff1o2 5380 fvmptss2 5504 fvmptssdm 5513 fprg 5611 dff1o6 5685 tposeq 6152 nntri1 6400 nntri2or2 6402 nnsseleq 6405 infnninf 7030 frec2uzf1od 10210 hashinfuni 10555 setsresg 12036 setsslid 12048 strle1g 12088 cncnpi 12436 hmeores 12523 limcimolemlt 12841 recnprss 12864 el2oss1o 13359 0nninf 13372 nninfall 13379 |
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