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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 3082 | . 2 | |
2 | 1 | simplbi 272 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wss 3041 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 |
This theorem is referenced by: eqimss2 3122 uneqin 3297 sssnr 3650 sssnm 3651 ssprr 3653 sstpr 3654 snsspw 3661 pwpwssunieq 3871 elpwuni 3872 disjeq2 3880 disjeq1 3883 pwne 4054 pwssunim 4176 poeq2 4192 seeq1 4231 seeq2 4232 trsucss 4315 onsucelsucr 4394 xp11m 4947 funeq 5113 fnresdm 5202 fssxp 5260 ffdm 5263 fcoi1 5273 fof 5315 dff1o2 5340 fvmptss2 5464 fvmptssdm 5473 fprg 5571 dff1o6 5645 tposeq 6112 nntri1 6360 nntri2or2 6362 nnsseleq 6365 infnninf 6990 frec2uzf1od 10147 hashinfuni 10491 setsresg 11924 setsslid 11936 strle1g 11976 cncnpi 12324 hmeores 12411 limcimolemlt 12729 recnprss 12752 el2oss1o 13115 0nninf 13124 nninfall 13131 |
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