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Mirrors > Home > NFE Home > Th. List > sseq2d | Unicode version |
Description: An equality deduction for the subclass relationship. (Contributed by NM, 14-Aug-1994.) |
Ref | Expression |
---|---|
sseq1d.1 |
Ref | Expression |
---|---|
sseq2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1d.1 | . 2 | |
2 | sseq2 3293 | . 2 | |
3 | 1, 2 | syl 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wceq 1642 wss 3257 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 |
This theorem is referenced by: sseq12d 3300 sseqtrd 3307 funimass2 5170 fnco 5191 fnssresb 5195 f1ores 5300 foimacnv 5303 fvelimab 5370 |
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