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Mirrors > Home > ILE Home > Th. List > eqriv | Unicode version |
Description: Infer equality of classes from equivalence of membership. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqriv.1 |
Ref | Expression |
---|---|
eqriv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2133 | . 2 | |
2 | eqriv.1 | . 2 | |
3 | 1, 2 | mpgbir 1429 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1331 wcel 1480 |
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-gen 1425 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-cleq 2132 |
This theorem is referenced by: eqid 2139 sb8ab 2261 cbvabw 2262 cbvab 2263 vjust 2687 nfccdeq 2907 difeqri 3196 uneqri 3218 incom 3268 ineqri 3269 difin 3313 invdif 3318 indif 3319 difundi 3328 indifdir 3332 pwv 3735 uniun 3755 intun 3802 intpr 3803 iuncom 3819 iuncom4 3820 iun0 3869 0iun 3870 iunin2 3876 iunun 3891 iunxun 3892 iunxiun 3894 iinpw 3903 inuni 4080 unidif0 4091 unipw 4139 snnex 4369 unon 4427 xpiundi 4597 xpiundir 4598 0xp 4619 iunxpf 4687 cnvuni 4725 dmiun 4748 dmuni 4749 epini 4910 rniun 4949 cnvresima 5028 imaco 5044 rnco 5045 dfmpt3 5245 imaiun 5661 opabex3d 6019 opabex3 6020 ecid 6492 qsid 6494 mapval2 6572 ixpin 6617 dfz2 9123 infssuzex 11642 1nprm 11795 |
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