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Mirrors > Home > ILE Home > Th. List > sseq2i | Unicode version |
Description: An equality inference for the subclass relationship. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
sseq1i.1 |
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Ref | Expression |
---|---|
sseq2i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1i.1 |
. 2
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2 | sseq2 3194 |
. 2
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3 | 1, 2 | ax-mp 5 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-in 3150 df-ss 3157 |
This theorem is referenced by: sseqtri 3204 sseqtrdi 3218 abss 3239 ssrab 3248 ssintrab 3882 iunpwss 3993 iotass 5213 dffun2 5245 ssimaex 5598 pw1fin 6938 pw1dc0el 6939 ss1o0el1o 6941 isstructim 12526 isstructr 12527 issubm 12924 grpissubg 13133 issubrng 13546 bj-ssom 15146 ss1oel2o 15202 |
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