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Theorem dfss2f 3056
 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 3054 . 2
2 dfss2f.1 . . . . 5
32nfcri 2250 . . . 4
4 dfss2f.2 . . . . 5
54nfcri 2250 . . . 4
63, 5nfim 1534 . . 3
7 nfv 1491 . . 3
8 eleq1 2178 . . . 4
9 eleq1 2178 . . . 4
108, 9imbi12d 233 . . 3
116, 7, 10cbval 1710 . 2
121, 11bitri 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1312   wcel 1463  wnfc 2243   wss 3039 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-in 3045  df-ss 3052 This theorem is referenced by:  dfss3f  3057  ssrd  3070  ssrmof  3128  ss2ab  3133
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