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Theorem dfss2f 3184
 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 3182 . 2
2 dfss2f.1 . . . . 5
32nfcri 2426 . . . 4
4 dfss2f.2 . . . . 5
54nfcri 2426 . . . 4
63, 5nfim 1781 . . 3
7 nfv 1609 . . 3
8 eleq1 2356 . . . 4
9 eleq1 2356 . . . 4
108, 9imbi12d 311 . . 3
116, 7, 10cbval 1937 . 2
121, 11bitri 240 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1530   wceq 1632   wcel 1696  wnfc 2419   wss 3165 This theorem is referenced by:  dfss3f  3185  ss2ab  3254  rankval4  7555  ballotth  23112  ssrd  23141  ssrmo  23164  rabexgfGS  23187  sigaclcuni  23494  dvcosre  27844  itgsinexplem1  27851  stoweidlem52  27904 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-in 3172  df-ss 3179
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