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Theorem ssopab2dv 4781
Description: Inference of ordered pair abstraction subclass from implication. (Contributed by NM, 19-Jan-2014.) (Revised by Mario Carneiro, 24-Jun-2014.)
Hypothesis
Ref Expression
ssopab2dv.1
Assertion
Ref Expression
ssopab2dv
Distinct variable groups:   ,   ,

Proof of Theorem ssopab2dv
StepHypRef Expression
1 ssopab2dv.1 . . 3
21alrimivv 1720 . 2
3 ssopab2 4778 . 2
42, 3syl 16 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393  C_wss 3475  {copab 4509
This theorem is referenced by:  xpss12  5113  coss1  5163  coss2  5164  cnvss  5180  aceq3lem  8522  shftfval  12903  sslm  19800  ulmval  22775  clwlkswlks  24758  iseupa  24965  fpwrelmap  27556  dicssdvh  36913  coss12d  37759
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-in 3482  df-ss 3489  df-opab 4511
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