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Theorem ssoprab2g 25032
 Description: Inference of operation class abstraction subclass from implication. (Contributed by FL, 24-Jan-2010.)
Hypothesis
Ref Expression
ssoprab2g.1
Assertion
Ref Expression
ssoprab2g
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem ssoprab2g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssoprab2g.1 . . . . 5
21anim2d 548 . . . 4
322eximdv 1610 . . 3
43ssopab2dv 4293 . 2
5 dfoprab2 5895 . 2
6 dfoprab2 5895 . 2
74, 5, 63sstr4g 3219 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wex 1528   wceq 1623   wss 3152  cop 3643  copab 4076  coprab 5859 This theorem is referenced by:  oprabex2gpop  25036 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-oprab 5862
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