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Theorem r19.12sn 3436
 Description: Special case of r19.12 2422 where its converse holds. (Contributed by NM, 19-May-2008.) (Revised by Mario Carneiro, 23-Apr-2015.)
Hypothesis
Ref Expression
r19.12sn.1
Assertion
Ref Expression
r19.12sn
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem r19.12sn
StepHypRef Expression
1 r19.12sn.1 . 2
2 sbcralg 2836 . . 3
3 rexsnsOLD 3410 . . 3
4 rexsnsOLD 3410 . . . 4
54ralbidv 2326 . . 3
62, 3, 53bitr4d 209 . 2
71, 6ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wb 98   wcel 1393  wral 2306  wrex 2307  cvv 2557  wsbc 2764  csn 3375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-sbc 2765  df-sn 3381 This theorem is referenced by: (None)
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