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Mirrors > Home > ILE Home > Th. List > dfss2f | Unicode version |
Description: Equivalence for subclass relation, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 3-Jul-1994.) (Revised by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
dfss2f.1 | |
dfss2f.2 |
Ref | Expression |
---|---|
dfss2f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 2934 | . 2 | |
2 | dfss2f.1 | . . . . 5 | |
3 | 2 | nfcri 2172 | . . . 4 |
4 | dfss2f.2 | . . . . 5 | |
5 | 4 | nfcri 2172 | . . . 4 |
6 | 3, 5 | nfim 1464 | . . 3 |
7 | nfv 1421 | . . 3 | |
8 | eleq1 2100 | . . . 4 | |
9 | eleq1 2100 | . . . 4 | |
10 | 8, 9 | imbi12d 223 | . . 3 |
11 | 6, 7, 10 | cbval 1637 | . 2 |
12 | 1, 11 | bitri 173 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wcel 1393 wnfc 2165 wss 2917 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-in 2924 df-ss 2931 |
This theorem is referenced by: dfss3f 2937 ssrd 2950 ss2ab 3008 |
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