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Mirrors > Home > ILE Home > Th. List > sseq1i | Unicode version |
Description: An equality inference for the subclass relationship. (Contributed by NM, 18-Aug-1993.) |
Ref | Expression |
---|---|
sseq1i.1 |
Ref | Expression |
---|---|
sseq1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1i.1 | . 2 | |
2 | sseq1 3090 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 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: eqsstri 3099 eqsstrid 3113 ssab 3137 rabss 3144 uniiunlem 3155 prss 3646 prssg 3647 tpss 3655 iunss 3824 pwtr 4111 ordsucss 4390 elnn 4489 cores2 5021 dffun2 5103 funimaexglem 5176 idref 5626 ordgt0ge1 6300 prarloclemn 7275 bdeqsuc 13006 bj-omssind 13060 |
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