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Theorem dfss2f 3490
 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 3488 . 2
2 dfss2f.1 . . . . 5
32nfcri 2612 . . . 4
4 dfss2f.2 . . . . 5
54nfcri 2612 . . . 4
63, 5nfim 1921 . . 3
7 nfv 1708 . . 3
8 eleq1 2529 . . . 4
9 eleq1 2529 . . . 4
108, 9imbi12d 320 . . 3
116, 7, 10cbval 2022 . 2
121, 11bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184  wal 1393   wcel 1819  wnfc 2605   wss 3471 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-in 3478  df-ss 3485 This theorem is referenced by:  dfss3f  3491  ssrd  3504  ss2ab  3564  rankval4  8302  ssrmo  27520  rabexgfGS  27529  ballotth  28673  dvcosre  31909  itgsinexplem1  31955
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