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Mirrors > Home > ILE Home > Th. List > ssriv | Unicode version |
Description: Inference rule based on subclass definition. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
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ssriv.1 |
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Ref | Expression |
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ssriv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 2928 |
. 2
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2 | ssriv.1 |
. 2
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3 | 1, 2 | mpgbir 1339 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-in 2918 df-ss 2925 |
This theorem is referenced by: ssid 2958 ssv 2959 difss 3064 ssun1 3100 inss1 3151 unssdif 3166 inssdif 3167 unssin 3170 inssun 3171 difindiss 3185 undif3ss 3192 0ss 3249 difprsnss 3493 snsspw 3526 pwprss 3567 pwtpss 3568 uniin 3591 iuniin 3658 iundif2ss 3713 iunpwss 3734 pwuni 3934 pwunss 4011 omsson 4278 limom 4279 xpsspw 4393 dmin 4486 dmrnssfld 4538 dmcoss 4544 dminss 4681 imainss 4682 dmxpss 4696 rnxpid 4698 enq0enq 6414 nqnq0pi 6421 nqnq0 6424 zssre 8028 zsscn 8029 nnssz 8038 uzssz 8268 divfnzn 8332 zssq 8338 qssre 8341 rpssre 8368 ixxssxr 8539 ixxssixx 8541 iooval2 8554 ioossre 8574 rge0ssre 8616 fzssuz 8698 fzssp1 8700 uzdisj 8725 nn0disj 8765 fzossfz 8791 fzouzsplit 8805 fzossnn 8815 fzo0ssnn0 8841 bj-omsson 9422 |
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