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Mirrors > Home > ILE Home > Th. List > sseq12d | Unicode version |
Description: An equality deduction for the subclass relationship. (Contributed by NM, 31-May-1999.) |
Ref | Expression |
---|---|
sseq1d.1 |
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sseq12d.2 |
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Ref | Expression |
---|---|
sseq12d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1d.1 |
. . 3
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2 | 1 | sseq1d 3184 |
. 2
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3 | sseq12d.2 |
. . 3
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4 | 3 | sseq2d 3185 |
. 2
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5 | 2, 4 | bitrd 188 |
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 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3135 df-ss 3142 |
This theorem is referenced by: 3sstr3d 3199 3sstr4d 3200 ssdifeq0 3505 relcnvtr 5144 rdgisucinc 6380 oawordriexmid 6465 nnaword 6506 nnawordi 6510 sbthlem2 6951 isbth 6960 nninff 7115 infnninf 7116 infnninfOLD 7117 nnnninf 7118 nnnninfeq 7120 nnnninfeq2 7121 nninfwlpoimlemg 7167 ennnfonelemkh 12396 ennnfonelemrnh 12400 isstruct2im 12455 isstruct2r 12456 basis1 13212 baspartn 13215 eltg 13219 metss 13661 0nninf 14409 nnsf 14410 peano4nninf 14411 nninfalllem1 14413 nninfself 14418 |
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