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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqss 3112 | . 2 | |
2 | 1 | simplbi 272 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wss 3071 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-in 3077 df-ss 3084 |
This theorem is referenced by: eqimss2 3152 uneqin 3327 sssnr 3680 sssnm 3681 ssprr 3683 sstpr 3684 snsspw 3691 pwpwssunieq 3901 elpwuni 3902 disjeq2 3910 disjeq1 3913 pwne 4084 pwssunim 4206 poeq2 4222 seeq1 4261 seeq2 4262 trsucss 4345 onsucelsucr 4424 xp11m 4977 funeq 5143 fnresdm 5232 fssxp 5290 ffdm 5293 fcoi1 5303 fof 5345 dff1o2 5372 fvmptss2 5496 fvmptssdm 5505 fprg 5603 dff1o6 5677 tposeq 6144 nntri1 6392 nntri2or2 6394 nnsseleq 6397 infnninf 7022 frec2uzf1od 10179 hashinfuni 10523 setsresg 11997 setsslid 12009 strle1g 12049 cncnpi 12397 hmeores 12484 limcimolemlt 12802 recnprss 12825 el2oss1o 13188 0nninf 13197 nninfall 13204 |
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