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Theorem dfss2f 2936
 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.)
Hypotheses
Ref Expression
dfss2f.1
dfss2f.2
Assertion
Ref Expression
dfss2f

Proof of Theorem dfss2f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfss2 2934 . 2
2 dfss2f.1 . . . . 5
32nfcri 2172 . . . 4
4 dfss2f.2 . . . . 5
54nfcri 2172 . . . 4
63, 5nfim 1464 . . 3
7 nfv 1421 . . 3
8 eleq1 2100 . . . 4
9 eleq1 2100 . . . 4
108, 9imbi12d 223 . . 3
116, 7, 10cbval 1637 . 2
121, 11bitri 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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