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Theorem ssopab2dv 4200
 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:   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem ssopab2dv
StepHypRef Expression
1 ssopab2dv.1 . . 3
21alrimivv 1847 . 2
3 ssopab2 4197 . 2
42, 3syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1329   wss 3071  copab 3988 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-in 3077  df-ss 3084  df-opab 3990 This theorem is referenced by:  xpss12  4646  coss1  4694  coss2  4695  cnvss  4712  shftfvalg  10590  shftfval  10593  sslm  12416
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