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Theorem ralsns 3597
 Description: Substitution expressed in terms of quantification over a singleton. (Contributed by Mario Carneiro, 23-Apr-2015.)
Assertion
Ref Expression
ralsns
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ralsns
StepHypRef Expression
1 df-ral 2440 . . 3
2 velsn 3577 . . . . 5
32imbi1i 237 . . . 4
43albii 1450 . . 3
51, 4bitri 183 . 2
6 sbc6g 2961 . 2
75, 6bitr4id 198 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1333   wceq 1335   wcel 2128  wral 2435  wsbc 2937  csn 3560 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-v 2714  df-sbc 2938  df-sn 3566 This theorem is referenced by:  ralsng  3599  sbcsng  3618  rabrsndc  3627  omsinds  4580  ssfirab  6875  uzsinds  10334
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