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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 3120 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 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: eqsstri 3129 eqsstrid 3143 ssab 3167 rabss 3174 uniiunlem 3185 prss 3676 prssg 3677 tpss 3685 iunss 3854 pwtr 4141 ordsucss 4420 elnn 4519 cores2 5051 dffun2 5133 funimaexglem 5206 idref 5658 ordgt0ge1 6332 prarloclemn 7307 bdeqsuc 13079 bj-omssind 13133 |
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