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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 3127 | . 2 | |
2 | dfss2f.1 | . . . . 5 | |
3 | 2 | nfcri 2300 | . . . 4 |
4 | dfss2f.2 | . . . . 5 | |
5 | 4 | nfcri 2300 | . . . 4 |
6 | 3, 5 | nfim 1559 | . . 3 |
7 | nfv 1515 | . . 3 | |
8 | eleq1 2227 | . . . 4 | |
9 | eleq1 2227 | . . . 4 | |
10 | 8, 9 | imbi12d 233 | . . 3 |
11 | 6, 7, 10 | cbval 1741 | . 2 |
12 | 1, 11 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 wcel 2135 wnfc 2293 wss 3112 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-in 3118 df-ss 3125 |
This theorem is referenced by: dfss3f 3130 ssrd 3143 ssrmof 3201 ss2ab 3206 |
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